Download Chapter 4 Review

Geometry
Chapter 4 Review
Name:_________________________________
1. What are the lengths of the sides of this equilateral triangle?
Use the figure for Questions 2 – 54
2. What is m∠1?
3. What is m∠2?
4. What is m∠3?
5. If △DJL ≅ △EGS, which segment in △EGS
corresponds to ̅̅̅̅
𝐷𝐿 ?
6. What is the congruency statement of the triangles?
7. Given that KML  CBA, find the value of x.
8. Quadrilateral MNQP is made of two congruent
triangles. ̅̅̅̅
𝑁𝑃 bisects ∠N and ∠P. In the quadrilateral,
m∠N = 50 and m∠P = 100. What is the measure of ∠M?
9. Find the value of x.
10. Write a correct congruence statement for the triangles
shown.
Decide whether it is possible to prove that the triangles are congruent. If it is possible, name the correct reason. Some problems may
have more than one answer – name all that apply. If it is not possible to prove the triangles are congruent with the given information,
say “not possible.”
11.
L
12.
13. P
O
14.
U
Y
R
W
K
N
M
T
V
X
S
15. What are the missing coordinates of the triangle?
16. Find the value of x.
17. Find the value of x.
18. Find the measures of angle 1 and 2.
29◦
70
4x + 10
3x + 5
(3x – 10)
62◦
2
5x - 25
1
For numbers 20 – 22, complete each proof. Use the reasons word bank for help.
20. Given: PF  AD
A
F
D
AP  PD
Prove: AFP  DFP
Statements
P
Reasons
1.
1.
2. DFP and AFP are right angles
2.
3.
3. All right angles are congruent
4.
4.
5.
5.
6.
6.
Reasons Word Bank
Definition of Congruent Angles
Definition of Congruent Segments
Reflexive Property
Symmetric Property
Transitive Property
Given
Midpoint Thm.
Definition of a Bisector
Definition of Perpendicular
Alternate Interior Angles Thm.
Vertical Angles Thm.
SSS
SAS
ASA
AAS
HL
CPCTC
21. Given: AB  DB
AC  DC
Prove: A  D
A
Statements
Reasons
1.
1.
2.
2
3.
3.
4. BAC  ________
4.
5.
5.
B
C
D
T
22. Given: TV || XR
1
TR || XV
V
2
Prove: T  X
4
R
3
X
Statements
1.
2.
Reasons
1.
1  3
2
3.
3. Given
4.
4. Alternate Interior Angles Theorem
5.
5.
6.
6. ASA
7.
7.
Reasons Word Bank
Definition of Congruent Angles
Definition of Congruent Segments
Reflexive Property
Symmetric Property
Transitive Property
Given
Midpoint Thm.
Definition of a Bisector
Definition of Perpendicular
Alternate Interior Angles Thm.
Vertical Angles Thm.
SSS
SAS
ASA
AAS
HL
CPCTC