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GEOMETRY - White Plains Middle School...Challenge Use the information given in the diagram to ... 30...
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GEOMETRY Chapter 4: Triangles Name:_____________________________ Teacher:____________________________ Pd: _______
Transcript of GEOMETRY - White Plains Middle School...Challenge Use the information given in the diagram to ... 30...
GEOMETRY
Chapter 4: Triangles
Name:_____________________________
Teacher:____________________________
Pd: _______
Table of Contents
DAY 1: (Ch. 4-1 & 4-2) SWBAT: Classify triangles by their angle measures and side lengths. Pgs: 1-5 Use triangle classification to find angle measures and side lengths. Pgs: 6-7
DAY 2: (Ch. 4-2) SWBAT: Apply theorems about the interior and exterior angles of triangles. Pgs: 8-12 HW: Pgs: 13-15
DAY 3: (Ch. 4-8) SWBAT: Apply Properties of Equilateral and Isosceles Triangles. Pgs: 16-21 HW: Pgs: 22-23
DAY 4: (Ch. 4-3) SWBAT: Use properties of congruent triangles to solve for missing sides and/or angles Pgs: 24-29 Prove triangles congruent by using the definition of congruence. HW: Pgs: 30-32
DAY 5: (Ch. 4-4 to 4-5) SWBAT: Prove triangles congruent by using SSS, SAS, ASA , AAS, and HL. Pgs: 33-35 HW: Pgs: 36-37
REVIEW
Pgs: 38-48
1
Day 1: Sum of Interior Angles of Triangles
Warm – Up
Classifying Triangles by their Sides
2
Practice – Find the missing angle
1) 2) 3)
Algebraic Problems
Practice: Practice:
m ∡1 = _____
m ∡2 = _____
m ∡3 = _____
3
Example 3:
Example 4: The ratio of the measures of the angles of a triangle is 4:5:6. Find the measure of the angles and classify the triangle
as acute, right, or obtuse.
Practice:
Practice
Practice
4
Challenge
Find the measure of the angle indicated.
SUMMARY
5
Exit Ticket
1.
2.
6
Day 1: HW
7
13. The angle measures of a triangle are in the ratio of 5:6:7. Find the angle measures of the triangle.
14.
15.
16. If the measures, in degrees, of the three angles of a triangle are x, x + 10, and 2x − 6, the
triangle must be:
1) Isosceles
2) Equilateral
3) Right
4) Scalene
8
Day 2: Exterior Angles of Triangles
Warm - UP
1. Find the measure of the missing angles.
2.
9
Part I: Angle relationships in triangles. Find the measure of all angles in the triangles below.
Then answer the following questions and try to develop the theorems that represent these relationships.
After checking the theorems with your teacher, then complete the remaining examples.
a)
b) c)
10
Part II: Conclusions
1. Investigate the Triangle Sum Theorem and its corollaries
a) 62 + 71 + _____ = _____ (m∡
b) 23 + 27 + _____ = _____ (m∡
c) 90 + 37 + _____ = _____ (m∡
2. Investigate the Exterior Angles Theorem
a) 62 + 71 = _____ m b) 23 + 27 = _____ m c) 37 + ______ = _____ m
(m∡
What relationship do you notice?
In any triangle, the sum of the interior angles is equal to ___________
In a right triangle, the two acute angles are _________________.
In an equiangular triangle, all angles measure ___________
The exterior angle of a triangle is always equal to
Formula: ____ + _____ = ______
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Part III: Practice. Apply the new theorems to solve each problem
1. Solve for x.
2.
3.
4. Solve for m∡
12
Challenge
Use the information given in the diagram to
determine the m∡ .
SUMMARY Exit Ticket
2x2+3x-2
4x+3
x2+1
A D
B
C
13
Day 2 – HW
14
15
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Day 3 – The Isosceles and Equilateral Triangle
Warm – Up Find the measure of the missing angles
17
If all the angles are congruent in a triangle, then the measure of each angle is ___________.
Example 1 – Find the value of x
Practice:
2. Find the value of OP.
18
Example 1:
Example 2: Finding the Measure of an Angle
a.
a. 80 b. 55
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Example 3:
a. 40 b. 150
Example 4: Finding the Measure of an Angle
Find mG.
Practice: Finding the Measure of an Angle
Find mN.
20
Example 5: Finding the Measure of an Angle
Practice Word Problem: Finding the Measure of an Angle
21
Challenge
Find the value of x.
Exit Ticket
1.
2.
22
Day – 3 - Homework
5. 6.
1. 2.
3. 4.
23
11. 12. 13.
24
Day 4 – Congruent Triangles
Warm – UP
1.
2.
25
Geometric figures are congruent if they are the same size and shape. Corresponding angles and
corresponding sides are in the same _______________ in polygons with an equal number of _______.
Two polygons are _________ polygons if and only if their _________________ sides are _____________. Thus
triangles that are the same size and shape are congruent.
Ex 1: Name all the corresponding sides and angles below if
Corresponding Sides Corresponding Angles
26
Ex 2:
Ex 3:
27
Example 4:
Example 5:
28
Example 6:
Example 7: ∆ABC ∆DEF
Find the value of x
Find mF.
29
Challenge
SUMMARY
\\
Exit Ticket
30
Day 4 – HW
31
5.
6.
7.
32
8.
9.
10.
11.
33
Day 5 – Proving Triangle Congruent
DO NOW
Using the tick marks for each pair of triangles, name the method {SSS, SAS, ASA, or AAS} if any, that can be
used to prove the triangles congruent.
Example 1:
_____________________ _____________________
34
Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what other
information is needed.
Example 2:
_____________________ _____________________
Practice
Using the tick marks for each pair of triangles, name the method {SSS, SAS, ASA, or AAS} if any, that can be
used to prove the triangles congruent.
a) b) c)
d) e) f)
35
Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what other
information is needed.
_________ ___________
___________ ___________
__________ ___________
Challenge Exit Ticket
36
HOMEWORK
Using the tick marks for each pair of triangles, name the method {SSS, SAS, ASA, or AAS} if any, that can be
used to prove the triangles congruent.
1)________________________ 2)____________________ 3)_____________________
4)________________________ 5)______________________ 6)_____________________
7)________________________ 8)______________________ 9)_____________________
10)________________________ 11)____________________ 12)_____________________
37
Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what other
information is needed.
13)________________________ 14)____________________ 15)_____________________
16)________________________ 17)____________________ 18)_____________________
19)________________________ 20)____________________ 21)_____________________
22)________________________ 23)____________________ 24)_____________________
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Day 6 – Review for Test
a. b.
c. d.
39
e.
f.
g.
40
h.
I.
J. In ABC, is extended to D, m B = 2y, m BCA = 6y, and m ACD = 3y. What is m A?
41
K.
L.
M-N.
42
O.
Given:
P.
43
Q. Given: ∡ ∡ ∡ ∡
∆JKM ∆ _______ because of ______.
R.
∆XWZ ∆ _______ because of ______.
S.
44
Determine if you can use SSS, SAS, ASA, AAS, and HL to prove triangles congruent. If not, say no.
Identifying Additional Congruent Parts
A.
B.
C.
D.
a.
b.
c.
d.
T ODA
MODA
OMAN
T OND
T ODA
MN
OA
MA
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a.
b.
c.
d.
a.
b.
c.
d.
What additional information is needed for a HL congruence correspondence?
a.
b.
c.
d.
OA
MA
NO
MONA
JC
KE
KAEL
AL
CADBAD
CB
ADAD
ACAB
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3.
47
7. In the accompanying diagram of BCD, ABC is an equilateral triangle and AD = AB. What is the value of x,
in degrees?
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Word Problems
1.
2.
3. F
4.
