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Geometry
Chapter 4 Review
2015-2016
How To Guide
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4.1
4.2
4.3-4.5
4.6
4.8
Classifying Triangles
Angle Relationships in
Triangles
Triangle Congruence
Triangle Congruence:
CPCTC
Isosceles and
Equilateral Triangles
1
1
1
1
1
2
2
2
2
2
3
3
3
3
3
4
4
4
4
4
4.1: Question 1
Classify the triangles by angle
measure
∆𝐸𝐹𝐻
∆𝐹𝐻𝐺
4.1: Question 2
Classify the triangles by side length
∆𝐸𝐹𝐻
∆𝐻𝐹𝐺
4.1: Question 3
Find the side lengths of the
equilateral triangle
4.1: Question 4
∆𝐴𝐵𝐶 is isosceles, and 𝐴𝐵 ≅ 𝐴𝐶. 𝐴𝐵 =
1
1
5
( 𝑥 + ) and 𝐵𝐶 = ( − 𝑥). What is the
2
4
2
perimeter of ∆𝐴𝐵𝐶?
*Draw a picture*
4.2: Question 1
The measure of one acute angle in a
right triangle is 32°. What is the
measure of the other acute angle?
4.2: Question 2
Find 𝑚∠𝑀
4.2: Question 3
Find 𝑚∠𝑃
4.2: Question 4
In ∆ABC, m∠𝐵 is 5° less than
1
2
2
1
1
2
times m∠𝐴.
m∠𝐶 is 5° less than
times m∠𝐴. What is
m∠𝐴?
4.3-4.5: Question 1
Given ∆𝑃𝑄𝑅 ≅ ∆𝑆𝑇𝑊. Identify all pairs
of congruent corresponding parts.
4.3-4.5: Question 2
Show that the triangles are
congruent for 𝑥 = 4
Note: you need to support your explanation
with one of the congruence theorems
4.3-4.5: Question 3
Find the missing pieces of the proof
4.3-4.5: Question 4
A mailman has to collect
mail from mailboxes and A
and B and drop it off at the
post office at C.
Draw a diagram of the route
and label the measure of
the angles in the triangle
4.6: Question 1
What does CPCTC stand for?
4.6: Question 2
Write a two-column proof
4.6: Question 3
Write a two-column proof
4.6: Question 4
Write a two column proof
4.8: Question 1
Find NP
4.8: Question 2
Find 𝑚∠𝐺
4.8: Question 3
Find x
4.8: Question 4
Find y
4.1: Answer 1
∆𝐸𝐹𝐻 is obtuse
∆𝐹𝐻𝐺 is equiangular
4.1: Answer 2
∆𝐸𝐹𝐻 is isosceles
∆𝐻𝐹𝐺 is scalene
4.1: Answer 3
3𝑦 − 4 = 2𝑦 + 3
𝑦−4=3
𝑦=7
2 7 + 3 = 17
4.1: Answer 4
P=
A
1
2( x
2
+
P=x+
1
𝑥
2
B
5
2
−𝑥
1
5
)+(
4
2
1
5
+(
2
2
1
+4
C
P=
1 5
+
2 2
P =
6
2
P = 3
− x)
− x)
4.2: Answer 1
90 − 32 = 58°
4.2: Answer 2
3𝑦 + 1 + 2𝑦 + 2 = 48
5𝑦 + 3 = 48
5𝑦 = 45
𝑦=9
3 9 + 1 = 28°
4.2: Answer 3
4𝑥 2 − 32 = 2𝑥 2
−32 = −2𝑥 2
2
16 = 𝑥
4=𝑥
2
2(4) = 32°
4.2: Answer 4
𝑚∠𝐴 = 𝑥
𝑚∠𝐵 = 1.5𝑥 − 5
𝑚∠𝐶 = 2.5𝑥 − 5
𝑥 + 1.5𝑥 − 5 + 2.5𝑥 − 5 = 180
5𝑥 − 10 = 180
5𝑥 = 190
𝑥 = 38°
4.3-4.5: Answer 1
Pairs of Angles: ∠𝑃 ≅ ∠𝑆, ∠𝑄 ≅ ∠𝑇, ∠𝑅 ≅ ∠𝑊
Pairs of Sides: 𝑃𝑄 ≅ 𝑆𝑇, 𝑄𝑅 ≅ 𝑇𝑊, 𝑃𝑅 ≅ 𝑆𝑊
4.3-4.5: Answer 2
𝐼𝐻 = 3, 𝐼𝐽 = 5
By Reflexive PoC, 𝐻𝐽 ≅ 𝐻𝐽
By SSS ∆𝐺𝐻𝐽~∆𝐼𝐻𝐽
4.3-4.5: Answer 3
𝐴: 𝐺𝑖𝑣𝑒𝑛
B: ∠𝐽𝐾𝐿 ≅ ∠𝑀𝐿𝐾
C: Reflexive PoC
D: SAS
4.3-4.5: Answer 4
𝑚∠𝐴 = 35°
𝑚∠𝐵 = 99°
𝑚∠𝐶 = 46°
4.6: Answer 1
Corresponding Parts of Congruent
Triangles are Congruent
4.6: Answer 2
Statements
Reasons
𝑌𝑊 bisects 𝑋𝑍
𝑋𝑌 ≅ 𝑌𝑍
𝑋𝑊 ≅ 𝑊𝑍
𝑊𝑌 ≅ 𝑊𝑌
Given
Given
Def’n of bisect
Reflexive PoC
∆𝑌𝑋𝑊 ≅ ∆𝑌𝑍𝑊
∠𝑋𝑌𝑊 ≅ ∠𝑍𝑌𝑊
SSS
CPCTC
4.6: Answer 3
Statements
Reasons
𝑁𝑂 ∥ 𝑀𝑃, ∠𝑁 ≅ ∠𝑃
Given
∠𝑁𝑂𝑀 ≅ ∠𝑃𝑀𝑂
Alternate Interior Angles Th’m
𝑀𝑂 ≅ 𝑀𝑂
Reflexive PoC
∆𝑁𝑂𝑀 ≅ ∆𝑃𝑀𝑂
AAS
∠𝑂𝑀𝑁 ≅ ∠𝑃𝑂𝑀
CPCTC
𝑀𝑁 ∥ 𝑂𝑃
Converse Alt. Interior Angles Th’m
4.6: Answer 4
• Draw auxiliary line segment MK
Statements
𝐽𝐾 ≅ 𝑀𝐿,
𝐽𝑀 ≅ 𝐾𝐿
Reasons
Given
𝑀𝐾 ≅ 𝑀𝐾
Reflexive PoC
∆𝐾𝐿𝑀 ≅ ∆𝐾𝐽𝑀
SSS
∠𝐽 ≅ ∠𝐿
CPCTC
4.8: Answer 1
5𝑦 − 6 = 4𝑦 + 12
𝑦 − 6 = 12
𝑦 = 18
Plug it back in!
5 18 − 6 = 84
4.8: Answer 2
3𝑥 = 𝑥 + 44
2𝑥 = 44
𝑥 = 22
Plug it back in!
𝑚∠𝐺 = 22 + 44
𝑚∠𝐺 = 66°
4.8: Answer 3
52
= 26°
2
4.8: Answer 4
 2𝑥 + 40 = 180
 2𝑥 = 140
 𝑥 = 70
 110 2 = 55
 3𝑦 − 5 = 55
 3𝑦 = 60
 𝑦 = 20