Math 2 Unit 5 Worksheet 1 Name: Polygon Angle-Sum Theorems ...
Transcript of Math 2 Unit 5 Worksheet 1 Name: Polygon Angle-Sum Theorems ...
Math 2 Unit 5 Worksheet 1
Math 2 Unit 5 Worksheet 1 Name: Polygon Angle-Sum Theorems Date: Per:
[1-3] Find the sum of the angle measures of each polygon. 1. 2. 3. 12-gon
[4-6] Find the measure of one angle in each regular polygon. Round to the nearest tenth if necessary.
4. 5. 6. regular 15-gon [7-9] Find the missing angle measures.
7. 8. 9. [10-12] Find the measure of an EXTERIOR angle of each REGULAR polygon. Round to the nearest tenth if necessary.
10. Decagon 11. 16-gon 12. hexagon
Math 2 Unit 5 Worksheet 1
ππΒ°
ππΒ°
[13-15] Find the value of each variable.
13. π₯π₯ = _________ 14. π₯π₯ = _________ 15. π€π€ = _________ π¦π¦ = _________ π¦π¦ = _________ π¦π¦ = _________ π₯π₯ = _________ π§π§ = _________
[16-18] The measure of an EXTERIOR angle of a REGULAR polygon is given. Find the measure of an INTERIOR angle. Then find the NUMBER OF SIDES.
16. 120Β° 17. 18Β° 18. 12Β° Interior Angle: _________ Interior Angle: _________ Interior Angle: _________ Number of Sides: _______ Number of Sides: _______ Number of Sides: _______
19. A regular polygon has an interior angle with a measure of 150Β°. How many sides does the polygon have?
20. A regular polygon has an interior angle with a measure of 175Β°. How many sides does the polygon have?
21. Find the value of π₯π₯. Drawing is not to scale.
π¦π¦Β° π₯π₯Β°
103Β° 93Β°
87Β°
Math 2 Unit 5 Worksheet 2
Math 2 Unit 5 Worksheet 2 Name: Properties of Parallelograms Date: Per: [1-5] The given figures are all parallelograms. Solve for the variable(s) in each diagram, then state the property of parallelograms that allowed you to solve for the variable(s).
1. π₯π₯ = ____________
Property: _______________________________
_______________________________________
_______________________________________
2. π·π·π·π· = 2π₯π₯ + 2, π·π·π·π· = 3π₯π₯ + 1, π·π·πΈπΈ = 3π₯π₯ β 3, π·π·πΈπΈ = 2π₯π₯ + 6 π₯π₯ = ____________
Property: _______________________________
_______________________________________
_______________________________________
3. ππ = ____________
Property: _______________________________
_______________________________________
_______________________________________
4. π₯π₯ = ____________
π¦π¦ = ____________
Property: _______________________________
_______________________________________
_______________________________________
5. π₯π₯ = ____________ π¦π¦ = ____________
Property: _______________________________
_______________________________________
_______________________________________
Math 2 Unit 5 Worksheet 2
[6-11] Can you prove the quadrilateral is a parallelogram based on the given information? Explain. 6. 7.
_________________________ _________________________
_________________________ _________________________
_________________________ _________________________
8. 9. _________________________ _________________________ _________________________ _________________________ _________________________ _________________________
10. 11.
_________________________ _________________________ _________________________ _________________________ _________________________ _________________________
[12-15] For what values of π₯π₯ and π¦π¦ must each figure be a parallelogram?
12. π₯π₯ =________ 13. π₯π₯ =________
π¦π¦ =________ π¦π¦ =________
14. π₯π₯ =________ 15. π₯π₯ =________
π¦π¦ =________ π¦π¦ =________
16. A classmate draws a parallelogram for which one side is twice as long as the other. If one side is 26 units, what are all the possible lengths of the perimeter?
17. Complete the two-column proof.
Given: Parallelogram π΄π΄π΄π΄π΄π΄π·π· with π΄π΄π΄π΄οΏ½οΏ½οΏ½οΏ½ β π΄π΄π·π·οΏ½οΏ½οΏ½οΏ½ Prove: βπ΄π΄π·π·π΄π΄ β βπ΄π΄π΄π΄π·π·
Statement Reason
1. Parallelogram π΄π΄π΄π΄π΄π΄π·π· with π΄π΄π΄π΄ β π΄π΄π·π·
1. Given
2.
2. Opposite sides of parallelograms are congruent.
3. π·π·π΄π΄οΏ½οΏ½οΏ½οΏ½ β π΄π΄π·π·οΏ½οΏ½οΏ½οΏ½ 4.
3. 4. SSS
Math 2 Unit 5 Worksheet 3
5. List 3 things that are
TRUE about the
diagonals of a rhombus.
10. List 2 things that are
TRUE about the
diagonals of a rectangle.
Math 2 Unit 5 Worksheet 3 Name: Properties of Rhombuses, Rectangles, and Squares Date: Per:
[1-4] Decide whether the parallelogram is a rhombus, a rectangle, or a square. Explain. 1. 2.
_________________________ _________________________
_________________________ _________________________
_________________________ _________________________
3. 4. _________________________ _________________________ _________________________ _________________________ _________________________ _________________________
1. ____________________________________________________________________ 2. ____________________________________________________________________ 3. ____________________________________________________________________
[6-9] Find the measures of the numbered angles in each rhombus.
6. 7. ππβ 1 ______ ππβ 2 ______ ππβ 1 ______ ππβ 2 ______
ππβ 3 ______ ππβ 4 ______ ππβ 3 ______ ππβ 4 ______
8. 9. ππβ 1 ______ ππβ 2 ______ ππβ 1 ______ ππβ 2 ______ ππβ 3 ______ ππβ 4 ______ ππβ 3 ______ ππβ 4 ______
1. ____________________________________________________________________ 2. ____________________________________________________________________
[11-12] π»π»π»π»π»π»π»π» is a rectangle. Find the value of π₯π₯ and the length of each diagonal.
11. π»π»π»π» = 3π₯π₯ + 5 and π»π»π»π» = 5π₯π₯ β 9 12. π»π»π»π» = 3π₯π₯ + 7 and π»π»π»π» = 6π₯π₯ β 11
π₯π₯ = _______ π₯π₯ = _______
π»π»π»π» = ______ π»π»π»π» = ______
π»π»π»π» = ______ π»π»π»π» = ______
Math 2 Unit 5 Worksheet 3
[13-14] Classify each of the following parallelograms as a rhombus, a rectangle, or a square. Explain.
13. πππποΏ½οΏ½οΏ½οΏ½οΏ½ β πππποΏ½οΏ½οΏ½οΏ½ 14. π΄π΄π΄π΄οΏ½οΏ½οΏ½οΏ½ β π΅π΅π΅π΅οΏ½οΏ½οΏ½οΏ½ _________________________ _________________________
_________________________ _________________________
_________________________ _________________________
15. For what value of π₯π₯ is parallelogram ππππππππ a rhombus? 16. ππππ = 14. For what value of π₯π₯ is parallelogram ππππππππ a rectangle? Find ππππ and ππππ.
π₯π₯ = ______ π₯π₯ = ______ ππππ = _____ ππππ = _____
[17-24] For what value of π₯π₯ is the figure the given special parallelogram?
17. Rhombus π₯π₯ = _______ 18. Square π₯π₯ = _______
19. Rectangle π₯π₯ = _______ 20. Rhombus π₯π₯ = _______
21. Rhombus π₯π₯ = _______ 22. Rectangle π₯π₯ = _______
23. Rhombus π₯π₯ = _______ 24. Rectangle π₯π₯ = _______
Math 2 Unit 5 Worksheet 4
Math 2 Unit 5 Worksheet 4 Name: Properties of Trapezoids Date: Per:
Trapezoids [1-2] The given figures are trapezoids. Solve for the variable(s) in each diagram.
1. π₯π₯ = _______
π¦π¦ = _______
2. π₯π₯ = _______
[3-7] Find π₯π₯ and the length of the given segment in each trapezoid.
3. π₯π₯ = _________
πΊπΊπΊπΊοΏ½οΏ½οΏ½οΏ½ = _______
4. π₯π₯ = _________
πΉπΉπΉπΉοΏ½οΏ½οΏ½οΏ½ = _______
5. π₯π₯ = _________ πΆπΆπΆπΆοΏ½οΏ½οΏ½οΏ½ = _______
6. π₯π₯ = _________ πππποΏ½οΏ½οΏ½οΏ½ = _______
7. π₯π₯ = _________ πππποΏ½οΏ½οΏ½οΏ½οΏ½ = _______
(2π₯π₯)Β°
136Β° (2π¦π¦ + 100)Β°
(4π¦π¦ β 82)Β°
π₯π₯Β°
88Β°
πΆπΆ πΆπΆ
2π₯π₯
10
3π₯π₯ β 4
πΊπΊ πΊπΊ
πΉπΉ πΉπΉ
πΆπΆ πΆπΆ
4π₯π₯ + 1
10
6π₯π₯ β 2
πΊπΊ πΊπΊ
πΉπΉ πΉπΉ
2π₯π₯ β 1
3π₯π₯ β 6
25
πΆπΆ πΆπΆ
πΊπΊ
πΉπΉ
πΊπΊ
πΉπΉ
Math 2 Unit 5 Worksheet 4
Isosceles Trapezoids 8. What is true about an isosceles trapezoid that is not necessarily true about all trapezoids?
1. _____________________________________________________________________________________
2. _____________________________________________________________________________________
3. _____________________________________________________________________________________ [9-10] Find the measures of the numbered angles in each isosceles trapezoid.
9. ππβ 1= _______ 10. ππβ 1= _______
ππβ 2= _______ ππβ 2= _______
ππβ 3= _______ ππβ 3= _______
[11-12] Find the value of the ππ in each isosceles trapezoid.
11. ππ = _______ 12. ππ = _______
[13-12] Find the value(s) of the variable(s) in each isosceles trapezoid.
13. π₯π₯ = _______ 14. π₯π₯ = _______
π¦π¦ = _______
15. π₯π₯ = _______ 16. π΄π΄πΆπΆ = π₯π₯ + 5 π₯π₯ = _______ π΅π΅πΆπΆ = 2π₯π₯ β 2
17. Error Analysis. What is the error in the following reasoning? An iscoceles trapezoid has one pair of parallel sides and one pair of congruent sides. Therefore, an isoceles trapezoid is a parallelogram.
(5ππ + 3)Β° 48Β°
π΄π΄
π΅π΅
πΆπΆ
πΆπΆ
Math 2 Unit 5 Worksheet 4
18. Is it possible to draw an isoceles trapezoid with one pair of opposite angles congruent? Explain and include a drawing of your explanation.
[19-24] True/False. If false, draw a counter example.
19. True / False: Diagonals of a rhombus must be congruent.
20. True / False: All angles of a rectangle are congruent.
21. True / False: All sides of a rectangle are congruent.
22. True / False: The diagonals of a square form four right triangles.
23. True / False: A trapezoid cannot have a right angle.
24. True / False: The diagonals of a parallelogram biscet the angles.
Math 2 Unit 5 Worksheet 5
Math 2 Unit 5 Worksheet 5 Name: Mid-Unit Review Date: Per:
[1-6] Solve for the variables. Give the best name for each of the following based upon given information and calculations. {Names of Quadrilaterals are: Quadrilateral, Parallelogram, Rectangle, Rhombus, Square, Trapezoid, & Isosceles Trapezoid}
1. 1. π₯π₯ = ________ π¦π¦ = ________ Name: ____________________
2. 2. π₯π₯ = ________ π¦π¦ = ________ Name: ____________________
3. 3. π₯π₯ = ________
π¦π¦ = ________ π§π§ = ________ Name: ____________________
4. 4. π₯π₯ = ________
π¦π¦ = ________ ππ = ________ Name: ____________________
5. 5. π₯π₯ = ________ π¦π¦ = ________ ππ = ________ Name: ____________________
70Β°
5π₯π₯Β° 4π¦π¦Β°
π¦π¦Β°
π₯π₯Β°
37Β°
π¦π¦Β°
π₯π₯Β°
3π§π§ + 3
8π§π§ β 7
π₯π₯Β°
π¦π¦Β° 52Β° (5ππ + 1)
(8ππ β 11)
3ππ + 2
(7π₯π₯ β 19)Β°
24Β°
5ππ + 7
(5π₯π₯ + 3)Β°
π¦π¦Β°
Perimeter of Quadrilateral is 90 cm
Math 2 Unit 5 Worksheet 5
6. 6. π₯π₯ = ________ ππ = ________ Name: ____________________
7. Find the sum of the measures of the interior angles for the following convex polygon: 17-gon 7. _______________________
8. Find the measure of each interior angle for the following regular polygon: Decagon 8. _______________________
9. Find the measure of each interior angle for the following regular polygon: Pentagon 9. _______________________
10. Find the number of sides for a convex polygon whose interior angle sum is: 3060Β° 10. _______________________
11. Find the number of sides for the following regular polygons, given: The measure of each exterior angle is 7.5Β° 11. _______________________
π΅π΅ πΆπΆ
π·π· π΄π΄
2π₯π₯ β 2
3π₯π₯ β 3
2π₯π₯ + 1
(4ππ + 1)Β° (6ππ β 13)Β°
Math 2 Unit 5 Worksheet 5
12. Complete the below chart on the Properties of Quadrilaterals
[13-24] Write all, some, or no, then explain.
13. _______________ rectangles are squares. ___________________________________________________________________________________________
14. _______________ isosceles trapezoids are parallelograms.
___________________________________________________________________________________________
15. _______________ rhombuses are quadrilaterals.
___________________________________________________________________________________________
Property Parallelogram Rectangle Rhombus Square Trapezoid Sum of the interior angles is 360Β°
Two pairs of opposite sides are parallel.
Has exactly one pair of parallel sides.
Two pairs of opposite sides are congruent.
All sides are congruent.
Diagonals are congruent.
Diagonals are perpendicular.
A diagonal bisects two angles.
A diagonal forms two congruent triangles.
Diagonals bisect each other.
Opposite angles are congruent.
All angles are right angles.
Consecutive interior angles are supplementary.
Math 2 Unit 5 Worksheet 5
16. _______________ squares are triangles.
___________________________________________________________________________________________
17. _______________ rectangles are regular quadrilaterals. ___________________________________________________________________________________________
18. _______________ quadrilaterals have four congruent angles.
___________________________________________________________________________________________
19. _______________ rectangles are rhombuses.
___________________________________________________________________________________________
20. _______________ trapezoids have one pair of opposite sides parallel.
___________________________________________________________________________________________
21. _______________ trapezoids have two pairs of congruent sides.
___________________________________________________________________________________________
22. _______________ squares are regular quadrilaterals.
___________________________________________________________________________________________
23. _______________ trapezoids have four congruent sides.
___________________________________________________________________________________________
24. _______________ parallelograms have four congruent angles.
___________________________________________________________________________________________
Math 2 Unit 5 Worksheet 6
Math 2 Unit 5 Worksheet 6 Name: Using Coordinates to Classify Quadrilaterals Date: Per:
Tools to Classify when Graphing
Slope Formula A. Same Slope = Parallel B. Slopes Opposite Reciprocals = Perpendicular Midpoint Formula C. Same Midpoint = Bisect Each other Distance Formula D. Same length = Congruent
Quadrilaterals and Useful Properties
In each blank, write A, B, C, or D stating which formula should be used to verify each property.
Parallelogram ______Opposite Sides are Parallel ______Opposite Sides are Congruent ______Diagonals Bisect Each other ______One pair opposite sides congruent & parallel Rhombus (A parallelogram withβ¦) ______All sides congruent ______Diagonals Perpendicular Rectangle (A parallelogram withβ¦) ______Adjacent Sides perpendicular ______Diagonals Congruent Square (A parallelogram withβ¦) A property from Rhombus and rectangle Trapezoid ______One pair opposite sides parallel (not both) Isosceles Trapezoid (A trapezoid withβ¦) ______Legs Congruent ______Diagonals Congruent
Graph Work/Justification/Answer
1.
Best Classification: _____________________
Math 2 Unit 5 Worksheet 6
2.
Best Classification: _____________________
3.
Best Classification: _____________________
4.
Best Classification: _____________________
Math 2 Unit 5 Worksheet 6
5.
Best Classification: _____________________
6.
Best Classification: _____________________
7.
Best Classification: _____________________
Math 2 Unit 5 Worksheet 6
8.
Best Classification: _____________________
9.
Best Classification: _____________________
Math 2 Unit 5 Worksheet 7
Math 2 Unit 5 Worksheet 7 Name: Using Coordinate Geometry Date: Per: to Prove Properties of Quadrilaterals
[1-3] What are the coordinates of the vertices of each figure? 1. Rectangle with 2. Rectangle centered at the 3. Square with height π₯π₯
base ππ and height β origin with base 2ππ and height 2β
π΄π΄ ( ___, ___ ) π΅π΅ ( ___, ___ ) π·π· ( ___, ___ ) πΈπΈ ( ___, ___ ) π»π» ( ___, ___ ) πΌπΌ ( ___, ___ ) πΆπΆ ( ___, ___ ) π·π· ( ___, ___ ) πΉπΉ ( ___, ___ ) πΊπΊ ( ___, ___ ) π½π½ ( ___, ___ ) πΎπΎ ( ___, ___ )
[4-12] Determine the missing coordinates in the diagrams. Do not introduce any new variables.
4. 5. 6.
7. 8. 9.
10. 11. 12.
x
y
(π π ,ππ) (βπ π ,ππ)
( ___,ππ) ( ___, ___ )
y
(ππ,ππ)
(ππ,ππ)
( ___, ___ )
x
y
(π π , ππ)
( ___, ___ )
( ___, ___ )
(ππ,ππ) x
y
(ππ, β ππ ) ( ___, ___ )
x
y
(ππ + ππ,ππ) (ππ,ππ)
y
(ππ,ππ )
(ππππ,ππ )
(βππ,ππ ) x
y
(ππ, β ππ ) ( ___, ___ )
( ___, ___ ) ( ___, ___ ) x
y
(βππ, βππ) ( ___, ___ )
x
y
(ππ,ππ)
(ππ,ππ) ( ___, ___ )
( ___, ___ )
( ___, ___ )
Math 2 Unit 5 Worksheet 7
13. Find the missing coordinates and find the midpoint of each diagonal.
14. Quadrilateral FLEA is a parallelogram. Find the coordinates for points F and E.
a) Show opposite sides are parallel using ____________________________ (which formula)
b) Show opposite sides are congruent using ____________________________ (which formula)
c) Show diagonals bisect each other using ____________________________ (which formula)
( ___, ___ ) ( ππ, ππ )
( ππ,ππ ) ( ___, ___ )
ππ (______, ______)
π¬π¬ (______, ______)
x
y
π³π³ (ππ + ππ,ππ)
π¨π¨(βππ,ππ)
ππ
π¬π¬
Math 2 Unit 5 Review Worksheet
Math 2 Unit 5 Name: Review Worksheet Date: Per:
[1-20] Show all work for each problem. NOTE: Diagrams are not drawn to scale.
1. What is the value of π₯π₯? 2. Determine the value of π₯π₯. A. 540Β° A. 15
B. 390Β° B. 15.4 C. 150Β° C. 9 D. 120Β° D. 19.8
3. Determine the sum of the exterior angles of an octagon. A. 1440Β°
B. 1080Β° C. 360Β°
D. 135Β° 4. Determine the measure of each interior angle of a regular sided polygon with 9 sides. A. 1620Β°
B. 180Β° C. 1260Β°
D. 140Β° 5. Determine the measure of each exterior angle of a regular polygon with 12 sides. A. 30Β°
B. 150Β° C. 216Β°
D. 36Β° 6. The measure of an interior angle of a regular polygon is 162Β°. How many sides does the polygon have? A. 18 sides
B. 20 sides C. 16 sides
D. 10 sides 7. Determine the value of π₯π₯? A. 80Β° B. 40Β° C. 60Β° D. 20Β°
120Β°
π₯π₯Β°
100Β°
100Β° 140Β°
140Β°
100Β°
π₯π₯Β°
(8π₯π₯ + 1)Β°
(5π₯π₯ β 4)Β° 73Β°
95Β°
Math 2 Unit 5 Review Worksheet
8. Find the number of sides for a regular polygon if each exterior angle has a measure of 15Β°. A 2340
B. 180 C. 24
D. 26 9. If πΉπΉπΉπΉ = 30, find πΉπΉπΉπΉ. A. 12 B. 18 C. 15 D. 30
10. ππππππππ is a rhombus. Determine the value of π₯π₯. A. 110Β°
B. 55Β° C. 70Β° D. 35Β°
11. What are the values of the variables in the given parallelogram?
A. π₯π₯ = 7, π¦π¦ = 9 B. π₯π₯ = 7, π¦π¦ = 65 C. π₯π₯ = 5, π¦π¦ = 71 D. π₯π₯ = 3, π¦π¦ = 77
Rule/Property used to solve for: π₯π₯ π¦π¦
12. If πΉπΉπΎπΎπΎπΎπΎπΎ is a rhombus, and ππβ πΉπΉπΎπΎπΎπΎ = 70Β°, what is the measure of ππβ 1? A. 55Β°
B. 50Β° C. 35Β° D. 90Β° 13. Which statements are true for a parallelogram? Select all that apply.
A. ππβ π΄π΄ + ππβ π΅π΅ = 180Β° B. ππβ π΄π΄ + ππβ πΆπΆ = 180Β°
C. β π΄π΄ β β π·π· D. π΅π΅πΆπΆοΏ½οΏ½οΏ½οΏ½ β π΄π΄π·π·οΏ½οΏ½οΏ½οΏ½
E. β π΄π΄ β β πΆπΆ
12
F
J H
G
K
A
B C
D
N M
L K 1
Q P
V T
110Β° π₯π₯Β°
(2π¦π¦ + 16)Β° (6π₯π₯ β 8)Β°
(4π₯π₯ + 6)Β°
Math 2 Unit 5 Review Worksheet
14. Determine the length of πΉπΉπΎπΎοΏ½οΏ½οΏ½οΏ½ in the trapezoid shown. A. 26 B. 4 C. 13 D. 17 15. a) If ππβ π΄π΄ is 80Β°, find the measures of:
ππβ π΅π΅ = ______
ππβ πΆπΆ = ______
ππβ π·π· = ______
b) What type of quadrilateral is π΄π΄π΅π΅πΆπΆπ·π·? Be as specific as possible. _________________________________________________ 16. Determine the values of x and y. π₯π₯ = _________ π¦π¦ = _________
17. π΄π΄π΅π΅πΆπΆπ·π· is an isosceles trapezoid with midsegment πΈπΈπΉπΉοΏ½οΏ½οΏ½οΏ½. Determine the following:
ππ = _____________ πΈπΈπΉπΉ = ______________ π₯π₯ = ______________ ππβ π΄π΄π·π·πΆπΆ = _________
Rules/Properties used to solve for: π₯π₯ ππ
M N
L K
I H
4π₯π₯ + 1
5π₯π₯ + 2
27
(2π₯π₯ β 17)Β° A
C B
E
10
D
F 3ππ β 4
36
(3π₯π₯ + 2)Β°
52Β°
π¦π¦Β°
π₯π₯Β°
Rules/Properties used to solve for π₯π₯:
Rule/Property used to solve for π₯π₯:
4
10 A D
C B
6 6
Math 2 Unit 5 Review Worksheet
18. π΄π΄π΅π΅πΆπΆπ·π· is a parallelogram. Determine the following: π₯π₯ = _____________
π¦π¦ = _____________
19. π΄π΄π΅π΅πΆπΆπ·π· is a rhombus. Determine the following: π₯π₯ = _____________ π¦π¦ = _____________ ππ = _____________ π§π§ = _____________ 20. For rectangle ππππππππ find the coordinates of ππ (without using any new variables), and
find the midpoints of πππποΏ½οΏ½οΏ½οΏ½ and πππποΏ½οΏ½οΏ½οΏ½.
ππ ( ______ , ______ ) Midpoint of πππποΏ½οΏ½οΏ½οΏ½ ( ______ , ______ )
Midpoint of πππποΏ½οΏ½οΏ½οΏ½ ( ______ , ______ ) 21. For parallelogram π΄π΄π΄π΄πΎπΎπΎπΎ find the coordinates of π΄π΄ and πΎπΎ (without using any new variables), and
find the midpoints of π΄π΄πΎπΎοΏ½οΏ½οΏ½οΏ½ and πΎπΎπ΄π΄οΏ½οΏ½οΏ½οΏ½οΏ½ π΄π΄ ( ______ , ______ ) πΎπΎ ( ______ , ______ )
Midpoint of π΄π΄πΎπΎοΏ½οΏ½οΏ½οΏ½ ( ______ , ______ )
Midpoint of πΎπΎπ΄π΄οΏ½οΏ½οΏ½οΏ½οΏ½ ( ______ , ______ )
Rule/Property used to solve: π¦π¦
ππ
42
B
A D
C
E 2π₯π₯ + 9π¦π¦
15 β 3π¦π¦
π₯π₯
ππ (0,ππ)
y
x ππ (ππ, 0)
ππ ( ____ , ____ )
ππ (0, 0)
π₯π₯Β° D
C B
A
π¦π¦Β°
15ππ β 7
43Β°
12ππ + 20
π§π§Β°
Rule/Property used to solve for π₯π₯ and π¦π¦:
x
y
π΄π΄ (ππ + ππ, ππ)
πΎπΎ(βππ, 0) πΎπΎ( _____ , _____ )
π΄π΄( _____ , _____ )
Math 2 Unit 5 Review Worksheet
22. Plot the points π΄π΄(1, β 1), π΅π΅(2, β 4) and πΆπΆ(4, β 2)
A. Plot a fourth point π·π· in B. Plot a fourth point π·π· in C. Plot a fourth point π·π· in quadrant 4 that will make quadrant 3 that will make quadrant 1 that will a parallelogram. a parallelogram. make a parallelogram. 23. Determine whether each statement is ALWAYS, SOMETIMES, or NEVER true
Always Sometimes Never
A rectangle is a square.
A square is a rhombus.
A trapezoid is a parallelogram.
The diagonals of a parallelogram are perpendicular.
The sides of a parallelogram are congruent.
Explain why the quadrilateral formed is a parallelogram using the slope formula.
Explain why the quadrilateral formed is a parallelogram using the midpoint formula.
Explain why the quadrilateral formed is a parallelogram using the distance formula.
Math 2 Unit 5 Review Worksheet
24. Samantha must prove this theorem: If π΄π΄π΅π΅οΏ½οΏ½οΏ½οΏ½ β π·π·πΆπΆοΏ½οΏ½οΏ½οΏ½ and π΅π΅πΆπΆοΏ½οΏ½οΏ½οΏ½ β π·π·π΄π΄οΏ½οΏ½οΏ½οΏ½, then π΄π΄π΅π΅πΆπΆπ·π· is a parallelogram.
Which choice correctly fills in the blank line in the paragraph proof?
A. SAS
B. ASA
C. AAS
D. SSS
E. HL
F. CPCTC
π΄π΄π΅π΅οΏ½οΏ½οΏ½οΏ½ β πΆπΆπ·π·οΏ½οΏ½οΏ½οΏ½ and π΅π΅πΆπΆοΏ½οΏ½οΏ½οΏ½ β π·π·π΄π΄οΏ½οΏ½οΏ½οΏ½ because of given information. π΄π΄πΆπΆοΏ½οΏ½οΏ½οΏ½ β π΄π΄πΆπΆοΏ½οΏ½οΏ½οΏ½ by the reflexive property.
βπ΄π΄π΅π΅πΆπΆ β βπΆπΆπ·π·π΄π΄ by the__________ theorem. β 1 β β 4 and β 2 β β 3 because corresponding parts of
congruent triangles are congruent. π΄π΄π΅π΅οΏ½οΏ½οΏ½οΏ½ β₯ π·π·πΆπΆοΏ½οΏ½οΏ½οΏ½ and π΅π΅πΆπΆοΏ½οΏ½οΏ½οΏ½ β₯ π΄π΄π·π·οΏ½οΏ½οΏ½οΏ½ because if alternate interior angles are
congruent then the lines are parallel. π΄π΄π΅π΅πΆπΆπ·π· is a parallelogram by definition of parallelogram.
A
B C
D 2
3 4
1