Geometry Complete Unit 2 - High School Math Teachers€¦ · Unit 2 Lesson Plans Name _____...
Transcript of Geometry Complete Unit 2 - High School Math Teachers€¦ · Unit 2 Lesson Plans Name _____...
Complete Unit 2
Package
HighSchoolMathTeachers.com©2020
Table of Contents
Unit 2 Pacing Chart -------------------------------------------------------------------------------------------- 1
Geometry Unit 2 Skills List ---------------------------------------------------------------------------------------- 5
Unit 2 Lesson Plans -------------------------------------------------------------------------------------------- 6
Day 16 Bellringer -------------------------------------------------------------------------------------------- 33
Day 16 Activity -------------------------------------------------------------------------------------------- 35
Day 16 Practice -------------------------------------------------------------------------------------------- 38
Day 16 Exit Slip -------------------------------------------------------------------------------------------- 43
Day 17 Bellringer -------------------------------------------------------------------------------------------- 45
Day 17 Activity -------------------------------------------------------------------------------------------- 47
Day 17 Practice -------------------------------------------------------------------------------------------- 49
Day 17 Exit Slip -------------------------------------------------------------------------------------------- 55
Day 18 Bellringer -------------------------------------------------------------------------------------------- 57
Day 18 Activity -------------------------------------------------------------------------------------------- 60
Day 18 Practice -------------------------------------------------------------------------------------------- 63
Day 18 Exit Slip -------------------------------------------------------------------------------------------- 70
Day 19 Bellringer -------------------------------------------------------------------------------------------- 72
Day 19 Activity -------------------------------------------------------------------------------------------- 75
Day 19 Practice -------------------------------------------------------------------------------------------- 78
Day 19 Exit Slip -------------------------------------------------------------------------------------------- 85
Week 4 Assessment -------------------------------------------------------------------------------------------- 87
Day 21 Bellringer -------------------------------------------------------------------------------------------- 94
Day 21 Activity -------------------------------------------------------------------------------------------- 96
Day 21 Practice -------------------------------------------------------------------------------------------- 98
Day 21 Exit Slip -------------------------------------------------------------------------------------------- 103
Day 22 Bellringer -------------------------------------------------------------------------------------------- 105
Day 22 Activity -------------------------------------------------------------------------------------------- 108
Day 22 Practice -------------------------------------------------------------------------------------------- 111
Day 22 Exit Slip -------------------------------------------------------------------------------------------- 116
Day 23 Bellringer -------------------------------------------------------------------------------------------- 118
Day 23 Activity -------------------------------------------------------------------------------------------- 120
Day 23 Practice -------------------------------------------------------------------------------------------- 122
Day 23 Exit Slip -------------------------------------------------------------------------------------------- 126
Day 24 Bellringer -------------------------------------------------------------------------------------------- 128
Day 24 Activity -------------------------------------------------------------------------------------------- 130
Day 24 Practice -------------------------------------------------------------------------------------------- 133
Day 24 Exit Slip -------------------------------------------------------------------------------------------- 136
Week 5 Assessment -------------------------------------------------------------------------------------------- 138
Day 26 Bellringer -------------------------------------------------------------------------------------------- 145
Day 26 Activity -------------------------------------------------------------------------------------------- 148
Day 26 Practice -------------------------------------------------------------------------------------------- 151
Day 26 Exit Slip -------------------------------------------------------------------------------------------- 155
Day 27 Bellringer -------------------------------------------------------------------------------------------- 157
Day 27 Activity -------------------------------------------------------------------------------------------- 159
Day 27 Practice -------------------------------------------------------------------------------------------- 162
Day 27 Exit Slip -------------------------------------------------------------------------------------------- 165
Day 28 Bellringer -------------------------------------------------------------------------------------------- 167
Day 28 Activity -------------------------------------------------------------------------------------------- 169
Day 28 Practice -------------------------------------------------------------------------------------------- 172
Day 28 Exit Slip -------------------------------------------------------------------------------------------- 175
Day 29 Bellringer -------------------------------------------------------------------------------------------- 177
Day 29 Activity -------------------------------------------------------------------------------------------- 179
Day 29 Practice -------------------------------------------------------------------------------------------- 182
Day 29 Exit Slip -------------------------------------------------------------------------------------------- 185
Week 6 Assessment -------------------------------------------------------------------------------------------- 187
Unit 2 Test -------------------------------------------------------------------------------------------- 196
Unit 2 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 1
Unit Week Day CCSS Standards Objective I Can Statements
Unit 2 Angles
and Lines
Week 4 – Algebraic
Definitions 16
CCSS.MATH.CONTENT.HSG.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line
segment, based on the undefined notions of point, line, distance along a line, and
distance around a circular arc.
Know precise algebraic definitions of angle; complementary, supplementary
angles and angles on a straight line
I can give the precise algebraic definitions
complementary, supplementary angles and
angles on a straight line
Unit 2 Angles
and Lines
Week 4 – Algebraic
Definitions 17
CCSS.MATH.CONTENT.HSG.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line
segment, based on the undefined notions of point, line, distance along a line, and
distance around a circular arc.
Know precise algebraic definitions of angle; angles at a point
I can give precise algebraic definitions of angle at a
point
Unit 2 Angles
and Lines
Week 4 – Algebraic
Definitions 18
CCSS.MATH.CONTENT.HSG.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line
segment, based on the undefined notions of point, line, distance along a line, and
distance around a circular arc.
Know precise algebraic definitions of angle; Corresponding and alternate
angles
I can give algebraic definitions of
corresponding and alternate angles
Unit 2 Angles
and Lines
Week 4 – Algebraic
Definitions 19
CCSS.MATH.CONTENT.HSG.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line
segment, based on the undefined notions of point, line, distance along a line, and
distance around a circular arc.
Know precise algebraic definitions of angle; vertical and interior angles
I can give the precise algebraic definitions of
vertical and interior angles
Unit 2 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 2
Unit 2 Angles
and Lines
Week 4 – Algebraic
Definitions 20 Assessment Assessment Assessment
Unit 2 Angles
and Lines
Week 5 – Prove Geometric Theorems
21
CCSS.MATH.CONTENT.HSG.CO.C.9 Prove theorems about lines and angles.
Theorems include: vertical angles are congruent; when a transversal crosses
parallel lines, alternate interior angles are congruent and corresponding angles are
congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Prove that vertical angles are congruent
I can prove that vertical angles are congruent
Unit 2 Angles
and Lines
Week 5 – Prove Geometric Theorems
22
CCSS.MATH.CONTENT.HSG.CO.C.9 Prove theorems about lines and angles.
Theorems include: vertical angles are congruent; when a transversal crosses
parallel lines, alternate interior angles are congruent and corresponding angles are
congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Prove that alternate interior angles are congruent
I can prove that alternate interior angles are
congruent
Unit 2 Angles
and Lines
Week 5 – Prove Geometric Theorems
23
CCSS.MATH.CONTENT.HSG.CO.C.9 Prove theorems about lines and angles.
Theorems include: vertical angles are congruent; when a transversal crosses
parallel lines, alternate interior angles are congruent and corresponding angles are
congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Prove that corresponding angles are congruent
I can prove that corresponding angles are
congruent
Unit 2 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 3
Unit 2 Angles
and Lines
Week 5 – Prove Geometric Theorems
24
CCSS.MATH.CONTENT.HSG.CO.C.9 Prove theorems about lines and angles.
Theorems include: vertical angles are congruent; when a transversal crosses
parallel lines, alternate interior angles are congruent and corresponding angles are
congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Prove that points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's
endpoints.
I can prove that points on a perpendicular bisector of a
line segment are exactly those equidistant from the
segment's endpoints.
Unit 2 Angles
and Lines
Week 5 – Prove Geometric Theorems
25 Assessment Assessment Assessment
Unit 2 Angles
and Lines
Week 6 – Prove Algebraically
26
CCSS.MATH.CONTENT.HSG.CO.C.9 Prove theorems about lines and angles.
Theorems include: vertical angles are congruent; when a transversal crosses
parallel lines, alternate interior angles are congruent and corresponding angles are
congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Given an angle, use the algebraic properties to show that alternate, vertical and corresponding angles
among others are equal
Given an angle, I can use the algebraic properties to
show that alternate, vertical and corresponding angles among others are
equal
Unit 2 Angles
and Lines
Week 6 – Prove Algebraically
27
CCSS.MATH.CONTENT.HSG.GPE.B.5 Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given
line that passes through a given point).
Prove the slope criteria for parallel and perpendicular lines
I can prove the slope criteria for parallel and
perpendicular lines
Unit 2 Pacing Chart
HighSchoolMathTeachers.com ©2020 Page 4
Unit 2 Angles
and Lines
Week 6 – Prove Algebraically
28
CCSS.MATH.CONTENT.HSG.GPE.B.5 Prove the slope criteria for parallel and
perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given
line that passes through a given point).
Use slope criteria to solve geometric problems (e.g., find the equation of a
line parallel or perpendicular to a given line that passes through a given point).
I can use slope criteria to solve geometric problems (e.g., finding the equation
of a line parallel or perpendicular to a given
line that passes through a given point).
Unit 2 Angles
and Lines
Week 6 – Prove Algebraically
29
CCSS.MATH.CONTENT.HSG.GPE.B.6 Find the point on a directed line segment
between two given points that partitions the segment in a given ratio.
Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
I can find the point on a directed line segment
between two given points that partitions the segment
in a given ratio.
Unit 2 Angles
and Lines
Week 6 – Prove Algebraically
30 Assessment Assessment Assessment
Geometry Unit 2 Skills List Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 5
Geometry Unit 2 Skills List
Number Unit CCSS Skill
8 2 HSG.CO.C.9 Prove theorems about lines and
angles
9 2 HSG.GPE.B.5 Prove the slope criteria for parallel
and perpendicular lines
10 2 HSG.GPE.B.5
Use the slope criteria for parallel and
perpendicular lines to solve
geometric problems
11 2 HSG.GPE.B.6
Find the point on a directed line
segment that partitions the segment
in a given ratio
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 6
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 4 – Algebraic Definitions
Day: 16
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Mathematical Practice: CCSS.MATH.PRACTICE.MP6 Attend to precision.
Objective: Know precise algebraic definitions of angle; complementary, supplementary angles and angles on a straight line
I can statement: I can give the precise algebraic definitions complementary, supplementary angles and angles on a straight line
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will measure and identify supplementary and complementary angles. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 16 Day 16 Activities Day 16 Practice Day 16 Presentation Day 16 Exit Slip
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 7
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 8
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 4 – Algebraic Definitions
Day: 17
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Mathematical Practice: CCSS.MATH.PRACTICE.MP6 Attend to precision.
Objective: Know precise algebraic definitions of angle; angles at a point
I can statement: I can give precise algebraic definitions of angle at a point
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. Students will draw angles at a point then find out about their properties. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 17 Day 17 Activities Day 17 Practice Day 17 Presentation Day 17 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 9
Reflection:
Extra/Additional Resources:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 10
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 4 – Algebraic Definitions
Day: 18
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Mathematical Practice: CCSS.MATH.PRACTICE.MP6 Attend to precision.
Objective: Know precise algebraic definitions of angle; Corresponding and alternate angles
I can statement: I can give algebraic definitions of corresponding and alternate angles
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will measure and identify vertical and interior angles. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 18 Day 18 Activities Day 18 Practice Day 18 Presentation Day 18 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 11
Reflection:
Extra/Additional Resources:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 12
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 4 – Algebraic Definitions
Day: 19
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.A.1 Know precise definitions of angle, circle, perpendicular line, parallel line, and line segment, based on the undefined notions of point, line, distance along a line, and distance around a circular arc.
Mathematical Practice: CCSS.MATH.PRACTICE.MP6 Attend to precision.
Objective: Know precise algebraic definitions of angle; vertical and interior angles
I can statement: I can give the precise algebraic definitions of vertical and interior angles
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will measure and identify vertical and interior angles. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 19 Day 19 Activities Day 19 Practice Day 19 Presentation Day 19 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 13
Reflection:
Extra/Additional Resources:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 14
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 4 – Algebraic Definitions
Day: 20
Common Core State Standard: Assessment
Mathematical Practice: Assessment
Objective: Assessment
I can statement: Assessment
Procedures: Assessment
Materials: Assessment
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 15
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 5 – Prove Geometric Theorems
Day: 21
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Mathematical Practice: CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
Objective: Prove that vertical angles are congruent
I can statement: I can prove that vertical angles are congruent
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The students will use thin metal bars,or straight wires to see tha changes in size of vertically opposite angles. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 21 Day 21 Activities Day 21 Practice Day 21 Presentation Day 21 Exit Slip
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 16
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 17
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 5 – Prove Geometric Theorems
Day: 22
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Mathematical Practice: CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
Objective: Prove that alternate interior angles are congruent
I can statement: I can prove that alternate interior angles are congruent
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will use the concept of measuring to come upwith to prove the congruence of alternate interior angles 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 22 Day 22 Activities Day 22 Practice Day 22 Presentation Day 22 Exit Slip
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 18
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 19
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 5 – Prove Geometric Theorems
Day: 23
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Mathematical Practice: CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
Objective: Prove that corresponding angles are congruent
I can statement: I can prove that corresponding angles are congruent
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will use the concept of measuring to come upwith to prove the congruence of corresponding angles 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 23 Day 23 Activities Day 23 Practice Day 23 Presentation Day 23 Exit Slip
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 20
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 21
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 5 – Prove Geometric Theorems
Day: 24
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Mathematical Practice: CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
Objective: Prove that points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
I can statement: I can prove that points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 7. Students will prove the equality of the points on a perpendicular bisector to the end points of a line using a number of strings. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 24 Day 24 Activities Day 24 Practice Day 24 Presentation Day 24 Exit Slip
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 22
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 23
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 5 – Prove Geometric Theorems
Day: 25
Common Core State Standard: Assessment
Mathematical Practice: Assessment
Objective: Assessment
I can statement: Assessment
Procedures: Assessment
Materials: Assessment
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 24
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 6 – Prove Algebraically
Day: 26
Common Core State Standard: CCSS.MATH.CONTENT.HSG.CO.C.9 Prove theorems about lines and angles. Theorems include: vertical angles are congruent; when a transversal crosses parallel lines, alternate interior angles are congruent and corresponding angles are congruent; points on a perpendicular bisector of a line segment are exactly those equidistant from the segment's endpoints.
Mathematical Practice: CCSS.MATH.PRACTICE.MP3 Construct viable arguments and critique the reasoning of others.
Objective: Given an angle, use the algebraic properties to show that alternate, vertical and corresponding angles among others are equal
I can statement: Given an angle, I can use the algebraic properties to show that alternate, vertical and corresponding angles among others are equal
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will be able to verify that vertical angles are equal in preparation for the lesson 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 26 Day 26 Activities Day 26 Practice Day 26 Presentation Day 26 Exit Slip
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 25
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 26
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 6 – Prove Algebraically
Day: 27
Common Core State Standard: CCSS.MATH.CONTENT.HSG.GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Mathematical Practice: CCSS.MATH.PRACTICE.MP8 Look for and express regularity in repeated reasoning.
Objective: Prove the slope criteria for parallel and perpendicular lines
I can statement: I can prove the slope criteria for parallel and perpendicular lines
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will work in groups of four to discover the slope criteria of parallel lines by drawing three parallel lines and comparing the steepness 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 27 Day 27 Activities Day 27 Practice Day 27 Presentation Day 27 Exit Slip
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 27
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 28
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 6 – Prove Algebraically
Day: 28
Common Core State Standard: CCSS.MATH.CONTENT.HSG.GPE.B.5 Prove the slope criteria for parallel and perpendicular lines and use them to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
Mathematical Practice: CCSS.MATH.PRACTICE.MP1 Make sense of problems and persevere in solving them.
Objective: Use slope criteria to solve geometric problems (e.g., find the equation of a line parallel or perpendicular to a given line that passes through a given point).
I can statement: I can use slope criteria to solve geometric problems (e.g., finding the equation of a line parallel or perpendicular to a given line that passes through a given point).
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 28 Day 28 Activities Day 28 Practice Day 28 Presentation Day 28 Exit Slip
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 29
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 30
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 6 – Prove Algebraically
Day: 29
Common Core State Standard: CCSS.MATH.CONTENT.HSG.GPE.B.6 Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Mathematical Practice: CCSS.MATH.PRACTICE.MP5 Use appropriate tools strategically.
Objective: Find the point on a directed line segment between two given points that partitions the segment in a given ratio.
I can statement: I can find the point on a directed line segment between two given points that partitions the segment in a given ratio.
Procedures: 1. Students will complete the bellringer. 2. Students will work in groups of at least 4. Students will verify the formula for proportional division of a line. 3. The presentation will be used to look for misconceptions and encourage discussion. 4. Students will complete the exit slip before leaving for the day.
Materials: Bellringer 29 Day 29 Activities Day 29 Practice Day 29 Presentation Day 29 Exit Slip
Accommodations/Special Circumstances:
Technology:
Unit 2 Lesson Plans Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 31
Reflection:
Extra/Additional Resources:
Day 16 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 32
Unit: Unit 2 Angles and Lines
Course: Geometry
Topic: Week 6 – Prove Algebraically
Day: 30
Common Core State Standard: Assessment
Mathematical Practice: Assessment
Objective: Assessment
I can statement: Assessment
Procedures: Assessment
Materials: Assessment
Accommodations/Special Circumstances:
Technology:
Reflection:
Extra/Additional Resources:
Day 16 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 33
1. In the figure below identify the following types of angles:
(a) an acute angle
(b) an obtuse angle
(c) a right angle
(d) a straight angle
2. Name the angle represented below in four different ways.
3. Solve for the unknown in the following equations:
(a) 4𝑥 − 20 = 160 − 6𝑥
(b) 𝑥 − 50 = 40 − 2𝑥
∅
K
L M
A
B
C
D
E
O
Day 16 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 34
Answer Keys
Day 16:
1. (a) ∠AOB, ∠BOC, ∠COD, ∠DOE
(b) ∠AOD, ∠BOE
(c) ∠AOC,∠COE
(d) ∠ AOE
2. ∠L, ∠KLM, ∠MLK, ∠∅
3. (a) 𝑥 = 18
(b) 𝑥 = 30
Day 16 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 35
A
B
1. Measure angle AOB using a protractor and write down the angle measure.
2. Measure angle BOC and write down the angle measure.
3. Find the sum of angle AOB and angle BOC. Write down the sum.
A O
B
C
D
P
O R
Q
Day 16 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 36
4. Now measure angle AOC along line AC and compare the angle measure to the sum you got in 3 above.
What do you notice?
5. Similarly, measure angle AOD and angle COD and note down the two angle measures.
6. Find the sum of angle AOD and angle COD. Write down the sum. Compare this sum to the angle
measure AOC.
7. What can you say about the sum of angles along line AC after measuring the two angles above the
line and the two angles below the line?
8. Measure angle POQ and write down its measure.
9. Measure angle QOR and write down its measure.
10. Find the sum of angles POQ and QOR and write it down.
11. Now, measure angle POR and write down its measure. Compare the sum in 10 above and the
measure of angle POR. What do you notice?
Day 16 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 37
In this activity, students will discover complementary angles, supplementary angles and angles on a
straight line on their own. You will design a pair of angles accurately on two different A4 papers. One
paper labeled A containing a set of complementary angles and the other paper labeled B containing a
set of supplementary angles as shown below. You will be obliged to walk around the groups and assist
the students where necessary, especially in measuring the angles. Students will work on the activity in
groups of 4, and each group will require a protractor and two A4 papers, containing the two sets.
Answer Keys
Day 16:
1. The angles from all the pairs should be similar.
2. The angles from all the pairs should be similar.
3. The angle sum should be 180°
4. The sum is equal to angle AOC
5. The angles from all the pairs should be similar.
6. The sum is equal to angle AOC
7. Their sum is 180°
8. The angles from all the pairs should be similar.
9. The angles from all the pairs should be similar.
10. Their sum is 90°
11. They are equal
Day 16 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 38
Find the supplements of the angles in questions 1-5:
1. 67°
2. 111°
3. 44°
4. 57°
5.179°
Find the complements of the angles in questions 6-10
6. 89°
7. 23°
8. 66°
9. 1°
10. 90°
Day 16 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 39
11. The angle measure of a supplement of an angle is 12° more than twice the angle. Calculate the
measure of the two angles.
12. The angle measure of a complement of an angle is 4° more than thrice the angle. Calculate the
measure of the two angles.
Find the value of 𝑥 in the figures in questions 13-16. (Angles not drawn to scale)
13.
14.
15.
𝑥 + 20°
40° 60°
7𝑥
2𝑥 3𝑥
2𝑥 − 30°
3𝑥 + 60° 10°
Day 16 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 40
16.
In questions 17 and 18, identify whether the sum of the angle shown and the unknown angle is
supplementary or complementary.
17.
18.
𝑥 + 45°
𝑥 − 10° 3𝑥 − 60°
115° 𝑥
31°
𝑥
Day 16 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 41
Use the figure below to answer questions 19 and 20.
19. Identify two supplements of ∠𝑇𝑂𝑈
20. Identify a pair of complementary angles.
R
P O S
Q
T
U
Day 16 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 42
Answer keys
Day 16:
1. 113°
2. 69°
3. 136°
4. 123°
5. 1°
6. 1°
7. 67°
8. 24°
9. 89°
10. 0°
11. 56° 𝑎𝑛𝑑 24°
12. 68.5° 𝑎𝑛𝑑 21.5°
13. 𝑥 = 60°
14. 𝑥 = 15°
15. 𝑥 = 28°
16. 𝑥 = 41°
17. Supplementary
18. Complementary
19. ∠𝑄𝑂𝑈 𝑎𝑛𝑑 ∠𝑅𝑂𝑇
20. ∠𝑃𝑂𝑄 𝑎𝑛𝑑 ∠𝑄𝑂𝑅
Day 16 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 43
1. (a) Find the supplement of 153°
(b) Find the complement of 49°
2. In a given pair of complementary angles, the size of the larger angle is four times the size of the
smaller angle. Find the size of the two angles.
Day 16 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 44
Answer Keys
Day 16:
1. (a) 27°
(b) 41°
2. 72° and 18°
Day 17 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 45
1. What is the value of b given that AB is a straight line?
2. Use the figure below to answer the questions that follow.
a) What is the value of c?
b) What is the value of d?
3. a) If a and b are complementary angles and the value of a is 49°, what is the values of b?
b) If c and d are two supplementary angles and the value of d is 300, what is the value of c?
A B
b 600
c d 390
Day 17 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 46
Answer Key Day 17
1. 120°
2. a). 51°
b).90°
3. a).41°
4. b).150°
Day 17 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 47
1. Draw a straight line on a plain paper using a ruler and a pencil and mark any point on the line and
label it T.
2. Draw other two lines through point T as shown below.
3. Measure each angle at point T using a protractor and record their values.
4. Add the angles on one side of each straight line; what is their sum in each case?
5. Add the values you got in step 3. What is their sum?
T
T
Day 17 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 48
In this activity, we are required to draw a line and identify a fixed point in that line then draw other lines
through that point. Students are required to divide themselves into groups of at least three. Each group
is required to have a plain paper, a pencil, a ruler and a protractor.
Answer Keys
Day 17:
1-3. No response
4. 180°
5. 360°
Day 17 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 49
In questions 1- 7 find the angle marked by a letter:
1.
2.
3.
4.
a
800 870
230 c
960
1140 d
b
950 48
Day 17 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 50
5.
6.
7.
8.
520 1360
1070
e
790 1500
950 f
1200 1000
800 h
830
g
Day 17 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 51
9.
10.
Use the figure below to answer questions 11 – 13
11. What is the value of j?
12. What is the value of i?
13. Find the value of h.
720
h i
j
1330 1350
j
2740
470 i
Day 17 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 52
14. Find the value of the angle marked l?
15.Find the angle k.
Use the fig below to answer questions 16, 17 and 18.
16. What is the value of m?
17. Find the value of n.
18. What is the value of o?
3330
l
870
930 124
0
k
m 580
n o
Day 17 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 53
Use the figure below to answer questions 19 and 20.
Lines AB and CD are straight.
19. Find the value of r.
20. What is the value of s?
1180
540
A
B C
D
r s
Day 17 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 54
Answer Key
Day 14.
1. 90°
2. 217°
3.170°
4. 150°
5. 65°
6. 36°
7. 277°
8. 60°
9. 39°
10. 92°
11. 108°
12. 72°
13. 108°
14. 27°
15. 56°
16. 90°
17. 32°
18. 90°
19. 62°
20. 64°
Day 17 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 55
1. Find the value of angle a in the figure below.
1300
a 800
1000
Day 17 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 56
Answer Keys
Day 1:
1. 500
Day 18 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 57
1. Find the value of a in the diagrams below.
(a)
(b)
(c)
𝑎 + 10°
57° 72°
2𝑏 + 31° 44°
89°
3𝑐 + 42° 5𝑐 − 64°
42°
Day 18 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 58
2. Find the angle measure represented by the letter in each case.
(a)
(b)
112°
3𝑦
𝑦
2𝑦
2𝑦
140° 13𝑡
7𝑡
11𝑡
9𝑡
Day 18 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 59
Answer Keys
Day 18:
1. (a) 𝑎 = 41°
(b) 𝑏 = 8°
(c) 𝑐 = 20°
2.
(a) 𝑦 = 31°
(b) 𝑡 = 5.5°
Day 18 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 60
1. Place the ruler on the paper and draw two lines of about 5 inches on either side of the ruler. The lines
should appear as shown below.
2. Remove the ruler and observe the lines you have drawn. What relationship exists between the two
lines?
3. Draw another straight line using a ruler to cut across the two lines as shown below.
4. Label the angles formed as shown below.
a b
c d
f e
g h
Day 18 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 61
5. Using a protractor measure accurately each angle in the following pairs of angles: ∠𝑎 and ∠𝑒; ∠𝑐 and
∠𝑔; ∠𝑏 and ∠𝑓; ∠𝑑 and ∠ℎ .What do you notice about the measures of the angles in each pair?
6. Using a protractor measure each angle in the following pairs of angles: ∠𝑐 and ∠𝑓; ∠𝑑 and ∠𝑒. What
do you notice about the measure of the angles in each pair?
7. Using a protractor measure each angle in the following pairs of angles: ∠𝑎 and ∠ℎ; ∠𝑏 and ∠𝑔. What
do you notice about the angles in each pair?
Day 18 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 62
In this activity, students will identify the relationship between angles formed when a line intersects a
pair of parallel lines. Students will work in groups of 4. Each group will require a ruler with straight
edges, a protractor, a pencil and a plain paper.
Answer Keys Day 18:
1. No response
2. They are parallel
3. The line must be drawn using a ruler, and it must intersect the two lines.
4. No response
5. Different responses; the pairs are approximately equal
6. Different responses; the pairs are approximately equal
7. Different responses; the pairs are approximately equal
Day 18 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 63
In questions 1-5, find the alternate interior and alternate exterior angles represented by letters. The two
lines shown in each case are parallel.
1.
2.
3.
105°
𝑥 𝑦
51°
𝑥 𝑦
123°
𝑥
𝑦
Day 18 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 64
4.
5.
66°
𝑥 𝑦
109°
𝑥
𝑦
Day 18 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 65
Given that 𝐴𝐵⃗⃗⃗⃗ ⃗ is parallel to 𝐶𝐷⃗⃗⃗⃗ ⃗ and line q is parallel to line r. Use the diagram to answer questions 6-10.
t is in degrees.
6. Find the value of t if ∠4 = 2𝑡 + 8 and ∠8 = 80°.
7. Find the value of t if ∠1 = 3𝑡 − 12 and ∠12 = 60°
8. Find the value of t if ∠7 = 𝑡 − 15 and ∠14 = 45 − 2𝑡
9. Find the value of t if ∠1 = 5𝑡 − 10 and ∠9 = 2𝑡 + 50
10. Find the value of t if ∠6 = 20𝑡 − 4 and ∠15 = 10𝑡 + 16
q r
1 2
3 4
5 6
7 8
9 10
11 12
13 14
15 16
Day 18 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 66
In questions 11-15, calculate the value of y that makes 𝑁𝑃⃗⃗⃗⃗⃗⃗ is parallel to 𝑄𝑅⃗⃗ ⃗⃗ ⃗⃗ . The value of y is in degrees.
11.
12.
13.
Q 100° − 2𝑦
𝑦 − 20° N P
R
Q
60°
5𝑦 + 10°
N P
R
Q 80°
2𝑦 − 24°
N P
R
Day 18 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 67
14.
15.
If QR and ST are parallel, identify whether the angles in questions 16-19 in the figure below are
corresponding, alternate interior or alternate exterior angles.
Q
140°
2𝑦 + 60° N P
R
Q
140°
𝑦 + 30°
N P
R
1 2
3 4
5 6
7 8
Q
R
S
T
Day 18 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 68
16. ∠2 and ∠7
17. ∠3 and ∠6
18. ∠2 and ∠6
19. ∠3 and ∠7
20. Identify all congruent angles from the figure above.
Day 18 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 69
Answer keys
Day 18:
1. 𝑥 = 105°, 𝑦 = 75°
2. 𝑥 = 51°, 𝑦 = 129°
3. 𝑥 = 123°, 𝑦 = 57°
4. 𝑥 = 114°, 𝑦 = 66°
5. 𝑥 = 109°, 𝑦 = 71°
6. 𝑡 = 36°
7. 𝑡 = 24°
8. 𝑡 = 20°
9. 𝑡 = 20°
10. 𝑡 = 2°
11. 𝑦 = 22°
12. 𝑦 = 62°
13. 𝑦 = 40°
14. 𝑦 = 40°
15. 𝑦 = 110°
16. Alternate interior
17. Alternate exterior
18. Corresponding
19. Corresponding
20. ∠1 ≅ ∠5; ∠2 ≅ ∠6; ∠3 ≅ ∠7; ∠4 ≅ ∠8; ∠2 ≅ ∠7; ∠4 ≅ ∠5; ∠1 ≅ ∠8; ∠3 ≅ ∠6
Day 18 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 70
Calculate the size of the angles represented by letters on the diagram below. (Angles not drawn to scale)
123° 𝑥
𝑦 𝑧
72°
Day 18 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 71
Answer Keys
Day 18:
𝑥 = 57°, 𝑦 = 57°, 𝑧 = 108°
Day 19 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 72
1. Find the alternate interior and alternate exterior angles represented by letters. The two lines shown
in each case are parallel.
(a)
(b)
54° 126°
𝑥 𝑦
27°
153°
𝑥
𝑦
Day 19 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 73
(c)
2. Using your angle values in question 1(b) above, find the following sums:
(a) 153° + 𝑦
(b) 𝑥 + 27°
Day 19 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 74
Answer Keys
Day 19:
1. (a) 𝑥 = 126°, 𝑦 = 54°
(b) 𝑥 = 153°, 𝑦 = 27°
(c) 𝑥 = 33°, 𝑦 = 147°
2. (a) 180°
(b) 180°
Day 19 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 75
1. Place the ruler on the paper and draw two lines of about 5 inches on either side of the ruler.
2. Remove the ruler and draw another straight line using a ruler to cut across the two lines as shown
below.
3. Label the angles formed as shown below.
a b
c d
f e
g h
Day 19 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 76
4. Compare the positions of the following angles relative to each other: ∠𝑎 and ∠𝑑; ∠𝑏 and ∠𝑐; ∠𝑒 and
∠ℎ; ∠𝑓 and ∠𝑔. What do you notice about these positions?
5. Using a protractor measure accurately each angle in the following pairs of angles: ∠𝑎 and ∠𝑑; ∠𝑏 and
∠𝑐; ∠𝑒 and ∠ℎ; ∠𝑓 and ∠𝑔. What do you notice about the measure of one angle compared to the other
in these pairs ?
6. Using a protractor measure each angle in the two pairs of angles: ∠𝑑 and ∠𝑓; ∠𝑐 and ∠𝑒.
7. Now, find the sum of the angles in those pairs as ∠𝑑 + ∠𝑓 and ∠𝑐 + ∠𝑒. What is common about the
two sums.
Day 19 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 77
In this activity, students will discover some key properties of vertical and interior angles. Students will
work in groups of 4. Each group will require a ruler with straight edges, a protractor, a pencil and a plain
paper.
Answer Keys Day 19:
1. No response
2. No response
3. No response
4. The angles are opposite each other
5. Responses will differ on each angle measured; In each pair, the angles are equal
6. Responses will differ
7. They all add up to 180°
Day 19 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 78
In questions 1-5, find the value of the angle represented by the letters.
1.
2.
3.
𝑧 67°
t 59°
𝑎
77°
Day 19 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 79
4.
5.
In questions 6-10, find the value of the angle represented by the letter. In each case, the two lines
intersected by the transversal are parallel.
6.
ℎ 167°
𝑟
171°
x
127°
Day 19 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 80
7.
8.
9.
10.
y
118°
t
59°
d
103°
g
67°
Day 19 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 81
In questions 11-15, solve for x in the given figures. The two lines intersected by the transversal are
parallel.
11.
12.
13.
14.
ሺ𝑥 + 30ሻ°
119°
ሺ2𝑥 − 7ሻ°
ሺ4𝑥 − 11ሻ°
ሺ𝑥 − 60ሻ°
ሺ4𝑥 − 20ሻ°
ሺ5𝑥 − 14ሻ°
ሺ3𝑥 + 6ሻ°
Day 19 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 82
15.
Find the value of x and hence angle ∠AOB in questions 16-20.
16.
17.
ሺ40𝑥 − 4ሻ°
ሺ10𝑥 − 16ሻ°
A
O
B
ሺ𝑥 + 29ሻ°
ሺ2𝑥 − 9ሻ°
A
O B ሺ2𝑥 + 8ሻ°
ሺ𝑥 + 21ሻ°
Day 19 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 83
18.
19.
20.
A
O
B
ሺ3𝑥 + 21ሻ°
ሺ𝑥 + 63ሻ°
Day 19 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 84
Answer keys Day 19:
1. 𝑧 = 67°
2. 𝑡 = 59°
3. 𝑎 = 77°
4. ℎ = 167°
5. 𝑧 = 171°
6. 𝑥 = 53°
7. 𝑦 = 62°
8. 𝑡 = 121°
9. 𝑑 = 77°
10. 𝑔 = 113°
11. 𝑥 = 31°
12. 𝑥 = 33 °
13. 𝑥 = 52°
14. 𝑥 = 23.5°
15. 𝑥 = 4°
16. 𝑥 = 38°
∠𝐴𝑂𝐵 = 67°
17. 𝑥 = 13°
∠𝐴𝑂𝐵 = 146°
18. 𝑥 = 40°
∠𝐴𝑂𝐵 = 80°
19. 𝑥 = 21°
∠𝐴𝑂𝐵 = 84°
20. 𝑥 = 79°
∠𝐴𝑂𝐵 = 110°
Day 19 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 85
In the figure below, KM⃗⃗⃗⃗⃗⃗ and LN⃗⃗⃗⃗ ⃗ intersect at O.
(a) Find the value of y.
(b) Hence, find :
(i) ∠NOM
(ii) ∠KOL
ሺ𝑦 + 69ሻ°
ሺ2𝑦 + 2ሻ°
K
L
M
N
O
Day 19 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 86
Answer Keys
Day 19:
(a) 𝑦 = 67
(b) 35°
(c) 35°
87
High School Math Teachers
Geometry
Week 4 Assessment
©2020HighSchoolMathTeachers
88
Week 4
Weekly Assessments
89
Week #4 1. Identify the transformation involved in each case. a)
b)
2. Find the value of the angle marked with a letter. a) b)
3. Use the diagram below to answer the following questions. a) Which rigid motion maps the triangles above onto each other? b) Are the two triangles congruent?
4. Use the figure below to answer the questions that follow. a) Which angle forms alternate angles with 𝑘? b) Which angle forms corresponding angles with 𝑗?
88°
𝑎
𝑏 73° 130°
53°
𝑓 𝑒 𝑔
ℎ
𝑖 𝑗 𝑘
𝑙
90
5. 𝑎 and 𝑏 are supplementary angles. 𝑏 − 36 = 131°. a) Find the value of 𝑎. b) Find the value of 𝑏.
6. State whether the following figures are congruent. a) b)
91
Week 4 - KEYS
Weekly Assessments
92
Week #4 KEY 1. Identify the transformation involved in each case. a) Reflection
b) Translation
2. Find the value of the angle marked with a letter. a) 272° b) 49°
3. Use the diagram below to answer the following questions. a) Which rigid motion maps the triangles above onto each other? Translation b) Are the two triangles congruent? Yes
4. Use the figure below to answer the questions that follow. a) Which angle forms alternate angles with 𝑘? 𝑓 b) Which angle forms corresponding angles with 𝑗? 𝑒
88°
𝑎
𝑏 73° 130°
53°
𝑓 𝑒 𝑔
ℎ
𝑖 𝑗 𝑘
𝑙
93
5. 𝑎 and 𝑏 are supplementary angles. 𝑏 − 36 = 131°. a) Find the value of 𝑎. 13° b) Find the value of 𝑏.
167°
6. State whether the following figures are congruent. a) They are congruent b) They are not congruent
Day 21 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 94
1. Use the figure below to answer the questions that follow.
If DF and EG are straight lines and ∠𝐷𝑂𝐸 = 113°;
a) What is the value of ∠𝐺𝑂𝐹?
b) What is the value of ∠𝐸𝑂𝐹?
c) What is the value of ∠𝐷𝑂𝐺?
2. What is the value of the angle marked a below given that AB is a straight line?
3. If b and c are two supplementary angles and the value of b is 41°, what is the value of c?
D E
G F
113°
O
64° a
A B
Day 21 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 95
Answer Key Day 21.
1 a) 113°
b) 67°
c) 67°
2. 116°
3. 139°
Day 21 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 96
1. Using the marker pen, mark an arbitrary point on each metal bar close to their centers.
2. Place one metal bar over the other such that the points you made touch each other as shown below.
3. Adjust the metal bars to different angles and observe how the opposite angles behave.
4. Adjust the metal bars until they make an obtuse angle.
5. Compare the size of in 4 above with the size of the angle opposite to it. Which kind of angle is it?
6. Adjust the metal bars to reduce the size of the obtuse angle and observe what happens to the angle
opposite to it as you reduce. What happens to the angle in the opposite direction?
Day 21 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 97
In this activity, students are required to compare how the size of a vertical angle changes if the size of
the other vertical angle is changed. Students are required to divide themselves into groups of at least
three. Each group is required to have two thin metal bars and a marker pen.
Answer Keys
Day 21:
1-4. No response
5. The angle opposite to it is also an obtuse angle.
5. The opposite angle reduces its size.
Day 21 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 98
In the figure below AB and CD are straight lines and ∠𝐴𝑂𝐶 = 710. Use the figure to answer questions 1
to 3.
1. What is the size of ∠𝐴𝑂𝐷?
2. What is the size of ∠𝐵𝑂𝐶?
3. Compare the sizes of ∠𝐴𝑂𝐷 and ∠𝐵𝑂𝐶.
Use the figure below to answer questions 4 to 6. CD and FG are straight lines.
4. Find ∠𝐶𝑂𝐹.
5. What is the size of ∠𝐷𝑂𝐺?
6. Compare the sizes of ∠𝐶𝑂𝐹 and ∠𝐷𝑂𝐺.
167∘ C
D F
G
O
A
O
B C
D
71°
Day 21 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 99
Use the figure below to answer questions 7 to 9. HI and JK are straight lines which intersect at P.
7. Find ∠𝐼𝑃𝐽
8. What is the value of ∠𝐻𝑃𝐾?
9. Compare the sizes of ∠𝐼𝑃𝐽 and ∠𝐻𝑃𝐾
Use the figure below to answer questions 10 to 12. AB and CD are straight lines.
10. What is the value of the angle marked a?
90
H J
K I
P
A
B
C
D
a 37°
b
Day 21 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 100
11. What is the value of the angle marked b?
12. Compare the size of a and that of b.
In the figure below ST and UV are straight lines which intersect at M. Use the figure to answer questions
13,14 and 15.
13. Find ∠𝑈𝑀𝑇
14. Find ∠𝑆𝑀𝑉
15. Compare the size of ∠𝑈𝑀𝑇 and that of ∠𝑆𝑀𝑉.
Use the figure below to answer questions 16,17 and 18. AD and FG are straight lines.
S
T
U
V
59°
M
89°
A
D F
G
O
Day 21 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 101
16. Find ∠𝐴𝑂𝐹
17. Find ∠𝐷𝑂𝐺
18. Compare the sizes of ∠𝐴𝑂𝐹 and ∠𝐷𝑂𝐺
Use the figure below to answer questions 19 and 20. KL and MN are straight lines.
19. Find ∠𝐾𝑂𝑀 and ∠𝐿𝑂𝑁
20. Compare the two angles in 19 above.
147° K
L M
N
O
Day 21 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 102
Answer Keys
Day 21:
1. 109°
2. 109°
3. They are equal
4. 13°
5. 13°
6. They are equal
7. 171°
8. 171°
9. They are equal
10. 143°
11. 143°
12. They are equal
13. 121°
14. 121°
15. They are equal
16. 91°
17. 91°
18. They are equal
19. ∠𝐾𝑂𝑀 = 33° and ∠𝐿𝑂𝑁 = 33°
20. They are equal
Day 21 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 103
1. What is the relationship between the size of ∠𝐴𝑂𝐶 and the size of ∠𝐵𝑂𝐷 given that AB and CD are
straight lines.
B
A
C
D
O
Day 21 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 104
Answer Keys
Day 22:
1. ∠𝐴𝑂𝐶 = ∠𝐵𝑂𝐷
Day 22 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 105
1. Find the angles represented by letters in the figures below. In each case the two lines intersected by
the transversal are parallel.
(a)
(b)
(c)
57°
𝑥
66°
𝑦
136°
𝑧
Day 22 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 106
2. Find the value of y in the figures below given that NP⃡⃗⃗⃗ ⃗ ∥ QR ⃡⃗ ⃗⃗⃗⃗ in each case.
(a)
(b)
Q
ሺ24𝑦 − 16ሻ°
ሺ20𝑦 + 4ሻ°
N P
R
Q
ሺ𝑦 + 48ሻ°
ሺ2𝑦 − 12ሻ°
N P
R
Day 22 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 107
Answer Keys
Day 22:
1. (a) 𝑥 = 57°
(b) 𝑦 = 66°
(c) 𝑧 = 136°
2. (a) 𝑦 = 60°
(b) 𝑦 = 5°
Day 22 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 108
1. Place the ruler on the paper and draw two parallel lines of about 3 inches on either side of the ruler.
2. Remove the ruler and draw a transversal to intersect the parallel lines as shown below.
3. Now, label four angles exactly as shown below.
a b
d c
Day 22 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 109
4. What can you say about the position of the angles relative to the parallel lines?
5. Measure ∠𝑎 and ∠𝑑 accurately using a protractor. What do you notice about the measures of the two
angles?
6. Consider and note the position of ∠𝑎 relative to ∠𝑑.
7. Similarly, measure ∠𝑏 and ∠𝑐 accurately using a protractor. What do you notice about the measures
of the two angles?
8. Similarly, consider and note the position of ∠𝑏 relative to ∠𝑐.
9. Identify one key similarity between the two pairs of angles you have measured.
Day 22 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 110
In this activity, students will be able to verify that alternate interior angles are equal. Students will work
on the activity in groups of four. Each group will be required to have a plain paper, a ruler graduated in
inches, a pencil and a protractor.
Answer Keys
Day 22:
1. No response
2. No response
3. No response
4. They are located between the parallel lines
5. The angles are equal
6. This is to remind the students about the position of a pair of alternate angles
7. The angles are equal
8. This is to remind the students about the position of a pair of alternate angles
9. Angles in each pair have equal measures
Day 22 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 111
Use the parallelogram PQRS formed by the two pairs of parallel lines below to answer questions 1-5.
∠PQR = 77°.
1. Find ∠PQU
2. Find ∠QPS
3. Hence find ∠QPT
4. Compare ∠PQR to ∠QPT. What can you deduce about the measures of the two angles?
5. Similarly, compare ∠PQU to ∠QPS. What can you deduce from the measures of the two angles?
P
Q
S
R
77°
T
U
Day 22 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 112
Use the figure below to answer questions 6-12.
6. Find the value of x
7. Find the actual measure of ∠QTX
8. Find the actual measure of ∠RXT
9. Find ∠PTX
10. Find ∠SXT
11. Compare ∠RXT to ∠QTX. What do you deduce from the measures of the two angles?
12. Compare ∠PTX to ∠SXT. What do you deduce from the measures of the two angles?
T
ሺ12𝑥 − 8ሻ°
ሺ10𝑥 + 2ሻ°
P
R
Q
S X
Day 22 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 113
In the figure below, KL ∥ MN. The two pairs of parallel lines form parallelogram ABCD. ∠𝐵𝐴𝐷 = 61°.
13. Find ∠BAT
14. Find ∠ABC
15. Find ∠ABU
16. Compare ∠BAT to ∠ABC. What do you discover about the measures of the two angles?
17. Compare ∠ABU to ∠BAD. What do you discover about the measures of the two angles?
L
K M
N
A
B C
D
61°
T
U
Day 22 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 114
In the figure below EF is a transversal and AB∥ CD.
18. Find the value of 𝑥.
19. Find the actual measure of ∠BEF and hence find ∠AEF. Similarly, find the actual measure of ∠DFE
and hence find ∠CFE.
20. Compare ∠AEF to ∠DFE and also compare ∠CFE to ∠BEF. How are the two angles in each case
related?
E
ሺ5𝑥 + 13ሻ°
ሺ7𝑥 − 37ሻ°
A
C
B
D F
Day 22 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 115
Answer keys
Day 22:
1. ∠PQU = 103°
2. ∠QPS = 103°
3. ∠QPT = 77°
4. They have equal angle measures
5. They have equal angle measures
6. 𝑥 = 5°
7. ∠QXT = 52°
8. ∠RXT = 52°
9. ∠PTX = 128°
10. ∠SXT = 128°
11. They have equal angle measures
12. They have equal angle measures
13. ∠BAT = 119°
14. ∠ABC = 119°
15. ∠ABU = 61°
16. They are equal
17. They are equal
18. 𝑥 = 17°
19. ∠BEF = 82°; ∠AEF = 98°; ∠DFE = 98°; ∠CFE = 82°
20. The angles are congruent
Day 22 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 116
Use the parallelogram KLMN formed by the two pairs of parallel lines below to answer the questions
that follow. ∠LKN = 111°.
(1) Find ∠PKL
(2) Find ∠KLM and hence find ∠OLK
(3) Compare ∠PKL to ∠KLM. What can you deduce about the measures of the two angles?
(4) Similarly, compare ∠LKN to ∠OLK. What can you deduce about the measures of the two angles?
K
L
N
M
111°
P
O
Day 22 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 117
Answer Keys
Day 22:
1. ∠PKL = 69°
2. ∠KLM = 69°
∠OLK = 111°
3. ∠PKL = ∠KLM.
4. ∠LKN = ∠OLK
Day 23 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 118
Use the following diagram to answer the following questions
1. Write all pairs of corresponding angles
2. Write all pairs of supplementary angles sharing the same point
3. Write all pairs of supplementary angles that are not sharing the same point
4. Find the sum of angles 𝑚, 𝑥, 𝑝 and 𝑦.
5. Compare the sum of 𝑎 and 𝑟 and that of 𝑝 and 𝑥.
𝑎
𝑥 𝑦
𝑟
𝑚
𝑛
𝑝
𝑞
Day 23 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 119
Answer Keys
Day 23:
1. 𝑟 and 𝑝; 𝑞 and 𝑦; 𝑎 and 𝑚; and 𝑛 and x
2. 𝑎 and 𝑟; 𝑟 and 𝑞, 𝑞 and 𝑛, 𝑛 and 𝑎, 𝑚 and 𝑝; 𝑝 and 𝑦, 𝑦 and 𝑥, 𝑥 and 𝑚
3. 𝑞 and 𝑝, 𝑛 and 𝑚
4. 360°
5. 𝑎 + 𝑟 < 𝑝 + 𝑥.
Day 23 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 120
1. Place the ruler on the paper and draw two parallel lines (by sliding a set square along the ruler) of
about at least 3 inches apart.
2. Draw any line to intersect the two parallel lines.
3. Label all the angles formed
4. Measure all angles
5. Compare the angles and group together those that are equal. How many groups do you have?
6. From each group, Identify pairs of corresponding angles
7. Are the pairs equal?
Day 23 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 121
In this activity, students will use the concept of measuring to come up with to prove the congruence of
corresponding angles. We students will work in groups of 4. Each group should have a straight edge (a
ruler), a set square a pencil, a plain paper and a protractor.
Answer Keys Day 23:
1.- 2. No response
3.- 4. Responses will differ
5. Responses will differ; 2 groups
6. No response
7. Yes
Day 23 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 122
Use the following diagram to answer questions 1-7.
Given that ∠𝑛 = 63°;
1. Find the value of ∠𝑙 and ∠𝑔.
2. Find the value of ∠𝑚 and ∠𝑓.
3. Find the value of ∠𝑟 and ∠𝑘.
4. Find the value of ∠ℎ.
5. Compare the values of ∠𝑟 and ∠𝑓.
6. List all pairs of corresponding angles.
7. Deduce the property that each pair in 6 has.
ℎ 𝑘
𝑛 𝑟
𝑙 𝑚
𝑔 𝑓
Day 23 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 123
Use the following diagram to answer questions 8-20 if 𝑡 is a complement of 14°.
8. Find the value of ∠𝑡.
9. Determine the Supplement of ∠𝑡.
10. Find the value of angles 𝑠, 𝑙,𝑚 and 𝑛.
11. Find the value of angles ℎ, 𝑘, 𝑝 and 𝑔.
12. Find the value of angles 𝑞, 𝑟, 𝑑 and 𝑤.
13. Find the value of angles 𝑡, 𝑣, 𝑒 and 𝑓.
14. What is a right angle?
Day 23 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 124
15. List all angles less than a right angle.
16. List all angles more than right angle.
17. From the list in 15 above, select pairs that are corresponding angles.
18. Identify any common feature in each pair
19. From the list in 16 above, select pairs that are corresponding angles.
20. Identify any common feature in each pair
Day 23 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 125
Answer keys
Day 23:
1. ∠𝑙 = 117° and ∠𝑔 = 63°.
2. ∠𝑚 = 63° and ∠𝑓 = 117°
3. ∠𝑟 = 117° and ∠𝑘 = 63°
4. ∠ℎ = 63°
5. ∠𝑓 = ∠𝑟 = 117°
6. ℎ and 𝑙, 𝑘 and 𝑚, 𝑔 and 𝑛, and 𝑓 and 𝑟
7. In each pair, the angles are equal
8. 76°
9. 104°
10. 𝑠 = 76°, 𝑙 = 76°,𝑚 = 104° and 𝑛 = 104°.
11. ℎ = 76°, 𝑘 = 76°, 𝑝 = 104° and 𝑔 = 104°
12. 𝑞 = 76°, 𝑟 = 76°, 𝑑 = 104° and 𝑤 = 104°
13. 𝑡 = 76°, 𝑣 = 104°, 𝑒 = 104° and 𝑓 = 76°
14. An angle whose measure is 90°
15. ℎ, 𝑘, 𝑙, 𝑠, 𝑡, 𝑓, 𝑟 and 𝑞
16. 𝑔, 𝑝,𝑚, 𝑛, 𝑒, 𝑣, 𝑑 and 𝑤
17. ℎ and 𝑠, 𝑘 and 𝑙, 𝑠 and 𝑡, 𝑓 and 𝑟, 𝑙 and 𝑓, and 𝑡 and 𝑞, ℎ and 𝑞, and 𝑘 and 𝑟
18. They are equal
19. 𝑔 and 𝑚, 𝑝 and 𝑛, 𝑒 and 𝑤, 𝑣 and 𝑑 , 𝑔 and 𝑤, 𝑑 and 𝑝, 𝑛 and 𝑡, and 𝑚 and 𝑒
20. They are equal.
Day 23 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 126
Find the value of ∠𝑇𝑊𝑆 and ∠𝑊𝑉𝑅 hence compare their values?
𝑃
Q
R
S
T
123°
U
V
W
Day 23 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 127
Answer Keys
Day 23:
∠𝑇𝑊𝑆 = 123°; ∠𝑊𝑉𝑅 =123°
They are all equal
Day 24 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 128
Use the following diagram to answer the following questions
1.The ratio of AP:PC = 1:1. If AP= 2in, what is PC?
2. The ratio of AB:BD = 1:1. If AB= 16 in, what is AD?
3. The ratio of AT:CT = 2:1. If AT= 12in, what is CT?
4. The ratio of AT:CT = 2:1. If AT= 12in, what is AC?
5. G is the midpoint of AF. If AF is 14 in, what is the length of GF?
Day 24 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 129
Answer Keys
Day 24:
1. 2 𝑖𝑛
2. 32 𝑖𝑛
3. 6 𝑖𝑛
4. 6 𝑖𝑛
5. 7 in
Day 24 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 130
1. Cut the four feet string.
2. Make knots at a half feet from each end so that it leaves a 3 feet distance in between the notes.
3. Cut a 5 feet string and tie it to the center of the first string leaving a half feet one side and 4.5 feet on
the other side.
4. Cut a two 5.5 feet strings and tie each at the knots of the first string and also at a common point 4
feet length (from the common knot of the first and second string) on the second string. The diagram is
shown below.
0.5 feet
4.5 feet
0.5 feet
4 feet
0.5 feet
5 feet
5 feet
Day 24 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 131
5. Let four students, each hold each end of the strings as shown.
6. Each student should make sure that the string he/she is holding is slightly tight. Student 4 should
move left right and backward until the 3 strings attached to the first string are tight.
7. Let a fifth student measure the angle (using the protractor) between the two main strings, that is,
students 1 -3 and students 2-4 strings. What is the approximate size of each angle?
8. How may we refer to the students 2 - 4 string in relation to that of students 1-3?
0.5 feet
4 feet
0.5 feet
5 feet
5 feet
Student
1
Student
2
Student
3
Student
4
Day 24 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 132
This is a very interesting activity where students will prove the equality of the points on a perpendicular
bisector to the endpoints of a line using a number of strings. Students will be in groups of at least 7.
Each group is required to have a fairly long string, like 20 feet, blackboard protractor, that is, any
instrument that can measure a right angle.
Answer Keys Day 24:
1. - 6. No response
7. 90°
8. Perpendicular bisector
Day 24 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 133
In the figure below, CE is a perpendicular bisector of AB and CD = 12 in. Use it to answer questions 1 –
10.
1. Find the size of AD if DB is 8 in.
2. Find value of angle 𝐴𝐷𝐶.
3. Find the length of CB.
4. Find the size of AC.
5. Compare the size of AC and CB.
6. If angle 𝐴𝐶𝐵 = 67.38, find the size of angle DCB.
7. Identify if any, a rigid motion relation triangles ADC and DBC.
8. Explain your answer in 7.
9. Identify the existence or non-existence of congruence of triangles ADC and DBC.
10. Explain your answer in 9 above.
D A B
C
E
Day 24 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 134
In the figure below, TU is perpendicular to PR, PS = SR and QS = 6 in. Use it to answer questions 11 – 20.
11. Find the size of PS if SR is 9 in.
12. Find the ratio of PR to PS.
13. Find the length of PQ.
14. Find the size of RQ.
15. Compare the size of PQ and QR.
16. Find the size of angle 𝑄𝑆𝑅 giving reason(s).
17. Identify if any, a rigid motion relation triangles PQS and QRS.
18. Explain your answer in 17.
19. Identify the existence or non-existence of congruence of triangles ADC and DBC.
20. Explain your answer in 19 above.
Day 24 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 135
Answer keys
Day 24:
1. 8 in
2. 90°
3. 14.42 in
4. 14.42 in
5. They are equal
6. 33.69°
7. Reflection
8. Triangle ACB is symmetrical about CD
9. The true triangles are congruent
10. They are related due to a rigid transformation whose existence implies the existence of
congruence
11. 9 in
12. 2 ∶ 1
13. 10.82 𝑖𝑛
14. 10.82 𝑖𝑛
15. They are equal
16. 90° since UQ intersects PR perpendicularly
17. Reflection
18. Triangle PQR is symmetrical about SQ
19. The true triangles are congruent
20. They are related due to a rigid transformation whose existence implies the existence of
congruence
Day 24 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 136
Find the value of ST given that VT is the perpendicular bisector or SU and 𝑉𝑆 = 3 𝑖𝑛, 𝑈𝑇 = 6𝑐𝑚 and the
perimeter of triangle STU is 18 in. Compare ST and UT.
S
U
T V
Day 24 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 137
Answer Keys
Day 24:
𝑆𝑇 = 6𝑐𝑚
They are all equal
138
High School Math Teachers
Geometry
Week 5 Assessment
©2020HighSchoolMathTeachers
139
Week 5
Weekly Assessments
140
Week #5
1. Use the figure below to answer the
questions that follow.
a) Find the value ℎ. b) Find the value of 𝑗. c) Find the value of 𝑘.
2. Use the figure below to answer the questions that
follow.
a) Find the value of 𝑎. b) Find the value of 𝑏.
3. Use the figure below to answer the
questions that follow.
a) By corresponding angle property, what is the value 𝑓? b) By supplementary angles property, what is the value of 𝑐? c) By supplementary angles property, what is the value of 𝑑?
4. Use the figure below to answer the questions that follow. a) Find the value of 𝑒. b) Find the value of 𝑛. c) Find the value of 𝑟. d) Find the value of 𝑞.
𝑓 𝑒 113°
ℎ
𝑖 𝑗 𝑘
𝑙
79° 𝑎 𝑏
𝑐 𝑎 55°
𝑏
𝑓 𝑑
𝑚 𝑒 143°
𝑛
𝑡 𝑟 𝑞
𝑠
141
5. Identify the rigid motion involved in each case. a) b)
6. Use the figure below to answer the questions that follow. a) Find the value of 𝑑. b) Find the value of c. c) Find the value of 𝑎.
𝑐 𝑎
145°
𝑏
𝑑
142
Week 5 - KEYS
Weekly Assessments
143
Week #5 KEY
1. Use the figure below to answer the questions that follow. a) Find the value ℎ. 67° b) Find the value of 𝑗. 67° c) Find the value of 𝑘. 113°
2. Use the figure below to answer the questions that follow. a) Find the value of 𝑏. 101° b) Find the value of 𝑎. 79°
4. Use the figure below to answer the
questions that follow.
a) By corresponding angle property, what is the value 𝑓? 55° b) By supplementary angles property, what is the value of 𝑐? 125° c) By supplementary angles property, what is the value of 𝑑? 125°
4. Use the figure below to answer the questions that follow. a) Find the value of 𝑒. 37° b) Find the value of 𝑛. 37° c) Find the value of 𝑟. 37° d) Find the value of 𝑞. 143°
𝑓 𝑒 113°
ℎ
𝑖 𝑗 𝑘
𝑙
79° 𝑎 𝑏
𝑐 𝑎 55°
𝑏
𝑓 𝑑
𝑚 𝑒 143°
𝑛
𝑡 𝑟 𝑞
𝑠
144
5. Identify the rigid motion involved in each case. a) Glide reflection b) Translation
6. Use the figure below to answer the questions that follow. a) Find the value of 𝑑. 35° b) Find the value of c. 145° c) Find the value of 𝑎. 145°
𝑐 𝑎
145°
𝑏
𝑑
Day 26 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 145
1. Given that the pair of lines intersected by the transversal is parallel, find the value of the x in the
following figures.
(a)
(b)
(c)
ሺ2𝑥 + 17ሻ°
ሺ3𝑥 − 41ሻ°
ሺ11𝑥ሻ°
ሺ9𝑥 + 18ሻ°
ሺ𝑥 + 5ሻ°
ሺ91 − 𝑥ሻ°
Day 26 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 146
2. In the figure below,MN⃗⃗⃗⃗ ⃗⃗ and PQ⃗⃗⃗⃗ ⃗ intersect at O as shown.
(a) Find the value of r.
(b) Hence, find ∠MOP :
ሺ2𝑟 − 111ሻ°
ሺ𝑟 + 24ሻ°
M
P
N
Q
O
Day 26 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 147
Answer Keys
Day 26:
1. (a) 𝑥 = 58°
(b) 𝑥 = 9°
(c) 𝑥 = 43°
2. (a) 𝑟 = 135°
(b) ∠MOP = 21°
Day 26 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 148
1. Place the carbon paper between the two plain papers provided make sure they are carefully aligned.
2. Draw two intersecting lines (at any angle), PQ⃡⃗ ⃗⃗ and RS⃡⃗⃗⃗ on the top plain paper.
2. Label the intersection point O as shown below.
3. Label the two pairs of vertical angles as shown below.
4. Separate the two papers and on the duplicate, cut out carefully angles α ́ and β ́ using the pair of
scissors provided.
P
Q R
S
O
𝛽
P
Q R
S
O
𝛼 �́�
𝛽ሖ
Day 26 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 149
5. Place the cut out of angle α ́on angle 𝛼 on the original plain paper. What do you notice? What does
this suggest about the two angles?
6. Place the cut out of angle β ́on angle β on the original plain paper. What do you notice? What does
this suggest about the two angles?
Day 26 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 150
In this activity, students will be able to verify that vertical angles are equal in preparation for the lesson.
The students will work in groups of four. Each group will be provided with two A4 size plain papers, an
A4 size carbon paper, a pencil, a ruler, a pair of scissors.
Answer Keys
Day 26:
1. No response
2. No response
3. No response
4. No response
5. The cut outfits exactly on the angle suggesting that the angles are equal.
6. The cut outfits exactly on the angle suggesting that the angles are equal.
Day 26 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 151
Use the figure below to answer questions 1 - 11. PQ⃡⃗ ⃗⃗ and RS⃡⃗⃗⃗ are parallel. AB⃡⃗⃗⃗ ⃗ intersects the two parallel
lines at points K and L. We are given ∠LKQ = 𝛽.
1. Find the measure of ∠LKP in terms of 𝛽.
2. Find the measure of ∠KLS in terms of 𝛽.
3. Compare ∠KLS to ∠LKP. What do you discover about the two angles?
4. Find the measure of ∠KLR in terms of 𝛽.
5. Compare ∠LKQ to ∠KLR. What do you notice about the two angles?
6. Find the measure of ∠AKQ in terms of 𝛽.
7. Find the measure of ∠BLR in terms of 𝛽.
8. Compare ∠AKQ to ∠BLR . What do you conclude?
9. Find the measure of ∠AKP in terms of 𝛽.
10. Find the measure of ∠BLS in terms of 𝛽.
11. Compare ∠AKP to ∠BLS . What do you notice?
Day 26 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 152
Use the figure below to answer questions 12-15. Lines AB and CD intersect to form the angles shown
and ∠DOB = θ.
12. Find the measure of ∠AOD in terms of 𝜃.
13. Find the measure of ∠BOC in terms of 𝜃.
14. Compare ∠AOD to ∠BOC . What do you notice about these two angles?
15. Find the measure of ∠AOC in terms of 𝜃 using the measure of ∠AOD.
16. Compare ∠DOB to ∠AOC . What do you notice about these two angles?
Use the figure below to answer questions 17-20. JK⃡⃗ ⃗ and LM⃡⃗⃗⃗ ⃗ are parallel. PQ⃡⃗ ⃗⃗ intersects the two parallel
lines at points to form the angles shown and ∠KAP = 𝑝°.
17. Find the measure of ∠JAP in terms of 𝑝.
𝜃
A
B
C
D
O
Day 26 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 153
18. Find the measure of ∠BAK in terms of 𝑝.
19. Find the measure of ∠BAJ in terms of 𝑝 using the measure of ∠BAK you have found in question 18
above.
20. Compare ∠BAJ to ∠KAP and write done your conclusion about the measures of the two angles.
Day 26 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 154
Answer keys Day 26:
1. ∠𝐿𝐾𝑃 = 180° − 𝛽
2. ∠𝐾𝐿𝑆 = 180° − 𝛽
3. ∠𝐿𝐾𝑃 = ∠𝐾𝐿𝑆 = 180° − 𝛽; They are equal
4. ∠𝐾𝐿𝑅 = 𝛽
5.∠LKQ = ∠KLR = 𝛽; They are equal
6. ∠𝐴𝐾𝑄 = 180° − 𝛽
7. ∠𝐵𝐿𝑅 = 180° − 𝛽
8. ∠𝐴𝐾𝑄 = ∠𝐵𝐿𝑅 = 180° − 𝛽;They are congruent
9. ∠𝐴𝐾𝑃 = 𝛽
10. ∠𝐵𝐿𝑆 = 𝛽
11.∠AKP = ∠BLS = 𝛽; They are equal
12. 180° − 𝜃
13. 180° − 𝜃
14. They are equal
15. 𝜃
16. They are equal
17. 180° − 𝑝°
18. 180° − 𝑝°
19. 𝑝°
20. They are congruent
Day 26 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 155
In the figure below, KL⃡⃗⃗⃗ and MN⃡⃗⃗⃗⃗⃗ are parallel. PQ⃡⃗ ⃗⃗ intersects the two parallel lines at points A and B. We
are further given ∠BAL = θ.
(a) Find the measure of ∠ABN in terms of 𝜃.
(b) Using the expression for the measure of ∠ABN you have found in part (a) above, find the measure
of ∠ABM in terms of 𝜃.
(c) Compare ∠ABM to ∠BAL. What do you discover about the two angles?
A
K L
M B N
P
Q
𝜃
Day 26 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 156
Answer Keys
Day 26:
(a) ∠ABN = 180° − 𝜃
(b) ∠ABM = θ
(c) ∠ABM = ∠BAL = θ; The two angles are congruent.
Day 27 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 157
1. A straight line AB passes through points K(8,4) and L(4,2).
a) Find the slope of line AB.
b) Find the equation of line AB.
2. A straight line KL passes through points M(5,10) and N(7,6).
a) Find the slope of the line.
b) Find the equation of the line KL.
3. A Straight line AB passes through a point P(2,1). If the same line is subjected to a translation of 3 units
upwards, what will be the new coordinates of point P.
Day 27 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 158
Answer Key
Day 4
1 a) 1
2
b) y=𝑥
2
2 a) −2
b) 𝑦 = −2𝑥 + 20
3. (2,4)
Day 27 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 159
1. Position the set square and the ruler as shown below.
2. Holding the ruler and the set square in the same position, carefully draw a line along the edge AB of
the set square.
3. Holding the ruler in the same initial position, carefully slide the set square along edge CD of the ruler
to another position in the direction shown below.
Day 27 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 160
4. In the same way, holding the ruler and the set square in the same position, carefully draw a line along
the edge EF of the set square.
5. Leaving the ruler unmoved, carefully remove the set square and observe the pair of lines you have
drawn. What kind of lines are they?
6. Compare the steepness of one line with respect to the other. What is your conclusion about the
steepness of this pair of lines?
7. If you another line in the same way along position GH as shown below, what will be its steepness in
comparison with the pair of lines you have drawn previously?
8. What conclusion regarding the type of lines in relation to their steepness do you deduce from the
type of lines you have drawn in this activity?
C
D
G H
Day 27 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 161
In this activity, students will work in groups of four to discover the slope criteria of parallel lines by
drawing three parallel lines and comparing the steepness. The students in the respective groups will
require a pencil, a protractor, a set square and an A4 size plain paper. It is perceived that the students
have discussed the basic properties of parallel lines.
Answer Keys
Day 27:
1. No response
2. No response
3. No response
4. No response
5. Parallel lines
6. They have the same steepness.
7. It will have the same steepness.
8. If two or more lines are parallel, then they have the same steepness
Day 27 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 162
Two parallel lines AB and CD share a perpendicular bisector. Line AB passes through points A(3,4) and
B(5,3). Line CD passes through points C(-2,8) and D(0,7). The perpendicular bisector passes through
points Q(3,3) and R(4,5) Use this information to answer questions 1-6.
1. Find the slope of line AB.
2. What is the slope of line CD?
3. Compare the slope of line AB and that of line CD.
4. What is the slope of their perpendicular bisector?
5. Multiply the slope of line AB with that of the perpendicular bisector. What is their product?
6. Find the product of the slope of line CD and the slope of the perpendicular bisector.
Two lines, 𝐿1 and 𝐿2 are parallel to each other. 𝐿1 passes through points A(6,3) and B(4,6) while
𝐿2 passes through points C(4,7) and D(2,10). Use this information to answer questions 7-9.
7. Find the slope of 𝐿1
8. Find the slope of 𝐿1
9. Compare the slope of 𝐿1 and that of 𝐿2
Two lines 𝐿3 and 𝐿4 are perpendicular to each other. 𝐿3 passes through points E(5,8) and F(3,9) while 𝐿4
passes through points G(1,2) and the origin. Use this information to answer questions 10-12.
10. Find the slope of 𝐿3.
11. Find the slope of 𝐿4.
12. What is the product of the slope of 𝐿4 and that of 𝐿3?
Day 27 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 163
Lines ST and MN are parallel to each other. Line ST passes through points S(2,3) and T(5,9). Line MN Passes
through points M(3,4) and N(6,10). Use this information to answer questions 13 to 15.
13. Find the slope of line ST
14. Find the slope of line MN
15. Compare the slopes of the two lines.
Line PT crosses two lines 𝐿5 and 𝐿6 such that it makes a right angle with them. Line PT passes through
points P(4,7) and T(2,1), 𝐿5 passes through points A(12,9) and B(9,10) and 𝐿6 passes through points G(4,3)
and F(1,4). Use this information to answer questions 16 to 20.
16. Find the slope of line PT
17. Find the slope of 𝐿5
18. Find the product of the slope of line PT and the slope of 𝐿5
19. Find the slope of 𝐿6
20. Find the product of the slope of line QR and the slope of 𝐿6
Day 27 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 164
Answer Keys
Day 27:
1. −1
2
2. −1
2
3. They are equal.
4. 2
5. -1
6. -1
7. −3
2
8. −3
2
9. They are equal.
10. −1
2
11. 2
12. -1
13. 2
14. 2
15. They are equal
16. 3
17. −1
3
18. -1
19. −1
3
20. -1
Day 27 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 165
1. Two lines AB and CD are perpendicular to each other, and they intersect at a point V(3,6). Line CD
passes through a point U(6,15) while line CD passes through a point W(0,7).
a) What is the slope of line AB?
b) Find the slope of line CD
C) Find the product of slope of line AB and the slope of line CD.
Day 27 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 166
Answer Keys
Day 27:
1. a) 3
b) −1
3
c) -1
Day 28 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 167
1. Two lines AB and CD are such that and the former passes through points A(2,3) and B(4,7) while the
latter passes through points C(1,2) and D(4,8).
a) Find the slope of line AB
b) Find the slope of line CD.
2. Two lines DF and DH intersect at point D(3,2). Line DF and DH pass through the point F(5,4) and H(4,3)
respectively.
a) Find the slope of line DF
b)Find the slope of line DH
3. Find the slope of a line that is perpendicular to another whose slope is 3.
Day 28 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 168
Answer Key Day 4
1 a) 2
b) 2
2 a) 1
b) -1
3. −1
3
Day 28 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 169
1. Plot the x y plane with a scale of two bigger squares representing one unit as shown below.
2. Mark points ሺ1, −1ሻ and ሺ−2,1ሻ and label them A and B respectively.
Day 28 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 170
3. Join points A and B with a straight line as shown below.
4. Mark points ሺ−3,−1ሻ and (-1,2) and label C and D respectively.
5. Using a ruler and a pencil join points C and D with a straight line as shown below.
6. Label the point of intersection of lines AB and CD as F.
7. Identify any two points on line AB and use them to find the slope of line AB.
What do you get as the slope of line AB?
8. Identify any two points on line CD and use them to find the slope of line CD.
What do you get as the slope of line CD?
9. Multiply the slope of line CD with the slope of line AB. What is their product?
10. Using a protractor measure ∠𝐴𝐹𝐶. What the size of ∠𝐴𝐹𝐶?
Day 28 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 171
In this activity, students are required to draw two lines in x y-plane, find their slopes and measure the
angle between them. Students are required to work in groups of at least three. Each group is required to
have a ruler, a pencil, a graph paper and a protractor.
Answer Keys
Day 28:
1-6. No response
7. −2
3
8. 3
2
9. −1
10. 90°
Day 28 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 172
Use the following information to answer questions 1 and 2.
Line AB is parallel to CD and passes through the points A(1,2) and B(4,4).If line CD passes through point
Dሺ3,7ሻ;
1. Find the slope of line AB
2. Find the equation of line CD
Use the following information to answer questions 3 - 5.
Two perpendicular lines ST and SV intersect at a point S(3,4). Line ST passes through point T(5,5).
3. Find the slope of line ST.
4. Find the slope of the line SV
5. Find the equation of the line SV
Use this information to answer questions 6 - 7.
A Line defined by 𝑦 = 3𝑥 + 4 is perpendicular to line DF. If the coordinates of D is (2,4)
6. Find the slope of the line DF
7. Find the equation of the line DF
Use the rectangle to answer questions 8 – 13.
DEFG is a rectangle. Two vertices of the rectangle are 𝐷ሺ4,3ሻ and 𝐸ሺ7,1ሻ
8. Find the slope of side DE
9. What is the slope of the side GF?
10. Find the slope of the side EF
11. Find the equation of side EF
12. What is the slope of side DG?
Day 28 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 173
13. If a line is drawn such that it coincides with the side DG, what will be the equation of that line?
Use this information to answer questions 14 - 16
Lines TU and UV intersect perpendicularly at a point 𝑈ሺ−31,9ሻ. If the coordinates of T is ሺ−11,21ሻ.
14. Find the slope of the line TU
15. What is the slope of the line UV?
16. Find the equation of the line UV
Use the following information to answer question 17-19.
Line PR is parallel to line ST and passes through points 𝑃ሺ5,0ሻ and 𝑅ሺ2,9ሻ. Line ST passes through a point
𝑆ሺ2,3ሻ.
17. Find the slope of the line PR
18. What is the slope of the line ST?
19. Find the equation of the line ST.
20. Two perpendicular lines 𝐿1 and 𝐿2 intersect at a point 𝐴ሺ−11,−4ሻ. 𝐿1 passes through a point
𝐵ሺ3,5ሻ. Find the equation of 𝐿2
Day 28 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 174
Answer Keys Day 28:
1. 2
3
2. 𝑦 = 2
3𝑥 + 5
3. 1
2
4. -2
5. 𝑦 = −2𝑥 + 10
6. −1
3
7. 𝑦 = −1
3𝑥 +
14
3
8. −2
3
9. −2
3
10. 3
2
11. 𝑦 = 3
2𝑥 −
19
2
12. 3
2
13. 𝑦 = 3
2𝑥 − 3
14. 4
5
15. −5
4
16. 𝑦 = −5
4𝑥 −
119
4
17. −3
18. −3
19. 𝑦 = −3𝑥 + 9
20. 𝑦 = −14
9𝑥 −
190
9
Day 28 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 175
1. ABCD is a square. Two of its vertices are A(2,4) and B(4,1) as shown below.
Without drawing, find the equation of side BC
B(4,1)
A(2,4) C
D
Day 28 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 176
Answer Keys
Day 28:
1. 𝑦 =3
2𝑥 − 5
Day 29 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 177
1. Find the distance between the following points
(a). ሺ2,4ሻ and ሺ−6,4ሻ.
b).ሺ5,3ሻ, ሺ5, −2ሻ
c). ሺ3,8ሻ, ሺ−1, 2ሻ
2. The ratio of 𝑦 to 𝑝 is 3 ∶ 5. If 𝑝 = 35, find the value of 𝑦.
3. Jastine and Justo are to share 18 pieces of candy in the ratio 1: 2 respectively. How many more pieces
of candies do Justo get more than Jastine?
Day 29 Bellringer Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 178
Answer Key
Day 29
1. a). 8 units
b). 5 units
c). 7.211 units
2. 21
3. 6.
Day 29 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 179
1. Take out the rod, place it on the part and marks its ends on the paper. Label the marks as M1 and M2
respectively.
2. Place one end of the rod at M2 and the other end as a new mark, M3 where M3, M2and M1 must be
on the same straight line.
3. Continue in that manner until you get M6 with M1 to M6 all lying on the same straight line.
4. How marks do you have in total?
5. How many spaces between the marks are there?
6. Identify mark 3, how many marks spaces (of the size of the rod) are before Mark 3.
7. Identify mark 3, how many marks spaces (of the size of the rod) are after Mark 3.
8. Find the ratio between the value in 6 and that of 7 respectively.
9. Let M1, M2, …, M6 be on a line that is on 𝑥- axis where M1 is at the origin. What would be the
coordinates of M1?
10. Identify the coordinates of M1, M3, and M6.
Day 29 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 180
11. Taking P = M3, verify that the formula 𝑥 =𝑚𝑥2+𝑛𝑥1
𝑚+𝑛; 𝑦 =
𝑚𝑦2+𝑛𝑦1
𝑚+𝑛 is true if 𝑃ሺ𝑥, 𝑦ሻ is the
coordinates of M3.
Day 29 Activity Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 181
In this activity, we would like to verify the formula for proportional division of a line. Students will work
in groups of 4. Each group will require a plain paper, a standard measurement tool which is a small grass
rod (or small rod that can serve the purpose) of 2 into 3 in, pencil.
Answer Keys
Day 29:
1 – 3.No response
4. 6
5. 5
6. 2
7. 3
8. 2 ∶ 3
9. ሺ0,0ሻ
10. 𝑀1ሺ0,0ሻ, 𝑀3ሺ2,0ሻ, 𝑀6ሺ5,0ሻ
11.𝑃ሺ2,0ሻ; 𝑥 = 2, 𝑦 = 0, 𝑚: 𝑛 = 2: 3, 𝑥1 = 𝑦1 = 𝑦2 = 0; 𝑥2 = 5
𝑥 =𝑚𝑥2+𝑛𝑥1
𝑚+𝑛=
2ሺ5ሻ+3ሺ0ሻ
2+3= 2 𝑦 =
𝑚𝑦2+𝑛𝑦1
𝑚+𝑛=
2ሺ0ሻ+3ሺ0ሻ
3+2= 0
Day 29 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 182
Use the following information to answer questions 1 - 3.
Given the following endpoints of a line segment, 𝐴ሺ−3,−2ሻ and 𝐵ሺ6,−5ሻ, find the coordinates of the
point that devides the line in the following ratios.
1. 1 ∶ 2
2. 2 ∶ 1
3. 1 ∶ 1
Use the following information to answer questions 4 - 9.
Given the following endpoints of a line segment, 𝐶ሺ−8,−7ሻ and 𝐷ሺ8,1ሻ, find the coordinates of the
point that devides the line in the following ratios.
4. 1: 7
5. 1 ∶ 1
6. 5 ∶ 3
7. 3 ∶ 5
8. 1 ∶ 3
9. 2 ∶ 3
Day 29 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 183
Use the following information to answer questions 10 - 18
The following endpoints of a line segment are 𝑀ሺ−2,4ሻ and 𝑁. Point 𝑇ሺ4,−2ሻ divides the line in the
ratio 1: 1.
10. Find the coordinates of 𝑁.
11. Find the coordinates of a point that divides the line in the ratio 1 ∶ 5.
12. Find the coordinates of a point that divides the line in the ratio 1 ∶ 3.
13. Find the coordinates of a point that divides the line in the ratio 1 ∶ 2.
14. Find the coordinates of a point that divides the line in the ratio 2 ∶ 1.
15. Find the coordinates of a point that divides the line in the ratio 3 ∶ 1.
16. Find the coordinates of a point that divides the line in the ratio 5 ∶ 1.
17. Find the coordinates of a point that divides the line in the ratio 5 ∶ 7.
18. Find the coordinates of a point that divides the line in the ratio 11 ∶ 1.
Use the following information to answer questions 19 - 20
The following endpoints of a line segment are 𝑃ሺ−7,−5ሻ and 𝑄. Point 𝑆ሺ−3,1ሻ divides the line in the
ratio 2: 1.
19. Find the coordinates of a point Q.
20. If Q divides line PR in the ratio 3 ∶ 1, find the coordinates of a point R.
Day 29 Practice Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 184
Answer Keys
Day 29:
1. ሺ0, −3ሻ
2. ሺ3, −4ሻ
3. ሺ1.5, −3.5ሻ
4. ሺ−6,−6ሻ
5. ሺ0, −3ሻ 6. ሺ2, −2ሻ
7. ሺ−2,−4ሻ
8. ሺ−4,−5ሻ
9. ሺ4, −1ሻ
10. ሺ10,−8ሻ
11. ሺ0,2ሻ
12. ሺ1,1ሻ
13. ሺ2,0ሻ
14. ሺ6, −4ሻ
15. ሺ7, −5ሻ
16. ሺ8, −6ሻ
17. ሺ3, −1ሻ
18. ሺ9, −7ሻ
19. ሺ−1,4ሻ
20. ሺ1,7ሻ
Day 29 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 185
Find the coordinate of a point C dividing the line segment joining ሺ−1, −3ሻ and ሺ2,4ሻ in the ratio 1.2.
Day 29 Exit Slip Name ____________________________________
HighSchoolMathTeachers.com©2020 Page 186
Answer Keys
Day 27:
ሺ0, −1ሻ
187
High School Math Teachers
Geometry
Week 6 Assessment
©2020HighSchoolMathTeachers
188
Week 6
Weekly Assessments
189
Week #6 1. Use the graph below to answer the questions that follow.
Find the slope of line AB. b) Find the slope of line CD. c) Calculate slope of AB × slope of CD.
-3 -2 -1 0 1 2 3 4 𝒙
𝒚
𝟏
𝟐
𝟒
𝟑
−𝟏
−𝟐
−𝟑
𝑨
𝑩
𝑪
𝑫
190
2. Use the graph below to answer the questions that follow.
a) Find the slope of EF. b) Find the slope of GF.
-3 -2 -1 0 1 2 3 4 𝒙
𝒚
𝟏
𝟐
𝟒
𝟑
−𝟏
−𝟐
−𝟑
𝑭
𝑮
𝑬
𝑯
191
3. Use the diagram below to answer the questions
that follow.
a) Find the value of 𝑏.
b) Find the value of c.
4. Use the figure below to answer the questions
that follow.
a) Using the properties of angles on a straight line, find the value of 𝑘. b) Using the properties of angles on a straight line find the value of 𝑙.
5. Lines ST and UV are parallel. The equation of ST
is 2𝑦 = 3𝑥 − 4. Line UV passes through
point 𝑉ሺ7, −3ሻ.
a) Find the slope of line UV. b) Find the equation line UV.
6. Find the missing complementary angle.
a) 41° b) 89°
37° 𝑘
𝑙 𝑐 𝑎 𝑏
𝑑 25°
192
Week 6 - KEYS
Weekly Assessments
193
Week #6 KEY 1. Use the graph below to answer the questions that follow.
Find the slow of line AB. −1 b) Find the slop of line CD. 1 c) Calculate slope of AB × slope of CD. 1
-3 -2 -1 0 1 2 3 4 𝒙
𝒚
𝟏
𝟐
𝟒
𝟑
−𝟏
−𝟐
−𝟑
𝑨
𝑩
𝑪
𝑫
194
2. Use the graph below to answer the questions that follow.
a) Find the slope of EF.
−3
2
b) Find the slope of GF.
−3
2
-3 -2 -1 0 1 2 3 4 𝒙
𝒚
𝟏
𝟐
𝟒
𝟑
−𝟏
−𝟐
−𝟑
𝑭
𝑮
𝑬
𝑯
195
3. Use the diagram below to answer the questions
that follow.
a) Find the value of 𝑏.
25°
b) Find the value of 𝑐.
25°
4. Use the figure below to answer the questions
that follow.
a) Using the properties of angles on a straight line, find the value of 𝑘. 143° b) Using the properties of angles on a straight line find the value of 𝑙. 37°
5. Lines ST and UV are parallel. The equation of ST
is 2𝑦 = 3𝑥 − 4. Line UV passes through
point 𝑉ሺ7, −3ሻ.
a) Find the slope of line UV.
3
2
b) Find the equation line UV. 2𝑦 = 3𝑥 − 27
6. Find the missing complementary angle.
a) 41° 39° b) 89° 1°
37° 𝑘
𝑙 𝑐 𝑎
𝑏
𝑑 25°
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Questions:
1. In the figure below, identify all right angles.
2. Name the angle represented below in four different ways.
3. Find the complements of the following angles:
a) 6°
b) 77°
c) 45°
4. Find the supplements of the following angles:
a) 1°
b) 145°
c) 32°
A
B
C
D
E
O
∅
A
B C
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5. In a given pair of supplementary angles, the size of the larger angle is four times the size of the
smaller angle. Find the size of the two angles.
6. What is the value of c?
7. Find the value of g!
8. What is the value of a?
40 𝑐
80
g
𝑎 + 10°
45 70
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9. Define transversal line!
10. Find the value of x!
11. If x and y are two complementary angles and the value of x is 11°, what is the value of y?
12. Find the measure of < 𝐹𝑂𝐷!
70°
𝑥
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13. Find the value of y!
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14. Define interior angles!
15. Find the sum of angles a, n, q and r.
16. C is the midpoint of AB. If AB is 22 in what is the length of CB?
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17. If CE is a perpendicular bisector of AB and if DB is 10 cm, find the size of AD.
18. A straight line JK passes through points A(16,8) and B(8,4). Find the slope of line JK.
19. Find the slope of a line that is perpendicular to another whose slope is 7.
20. Find the distance between (1, -1) and (-7, 5).
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Answers:
1. ∠AOC, ∠COE
2. ∠B, ∠ABC, ∠CBA, ∠x
3.
a) 84°
b) 13°
c) 45°
4.
a) 179°
b) 35°
c) 148°
5. 144°and 36°
6. 𝑐 = 50°
7. 𝑔 = 280°
8. 𝑎 = 55°
9. Transversal line is a line that crosses two or more parallel lines at different points.
10. 𝑥 = 110°
11. y=79°
12. < 𝐹𝑂𝐷 = 89°
13. y=5
14. Interior angles are angles formed between a pair of parallel lines when a transversal line intersects
the pair of parallel lines.
15. 360°
16. CB = 11 in
17. AD = 10 cm
18. 𝑚 =1
2
19. 𝑚 = −1
7
20. 10 units