Chapter 5 Test Review
Geometry
Name:_________________________________
Use the diagram at the right.
1. List all corresponding congruent angles



2. List all corresponding congruent sides.



3. Are the triangles congruent? If so, give a congruence statement.
In the diagram ∆ALX ≅ ∆GIW, complete the following statements.
̅̅̅̅ ≅
4. 𝐿𝑋
5. ∠I ≅
6. ∠A ≅
7. ̅̅̅̅
𝐴𝐿 ≅
8. m ∠A =
9. IW =
10. ∆LAX ≅
For #11-19, decide whether enough information is shown to prove the triangles are
congruent. If so, state the postulate or theorem that you would use.
11.
12.
13.
______________________
______________________
______________________
14.
15.
16.
______________________
______________________
______________________
17.
______________________
18.
______________________
19.
______________________
20.
̅̅̅̅ ≅ 𝑅𝑆
̅̅̅̅, 𝑄𝑅
̅̅̅̅ ≅ 𝑆𝑃
̅̅̅̅
Given: 𝑃𝑄
Prove: ∆PQR ≅ ∆RSP
Statements
1. ̅̅̅̅
𝑃𝑄 ≅ ̅̅̅̅
𝑅𝑆
Reasons
1. ________________________
2.
2. Given
3. _____________________________
3. Reflexive
4. ∆PQR ≅ ∆RSP
4.
21.
Given: ̅̅̅̅
𝐴𝐶 bisects ∠BAD, ∠B ≅ ∠D
̅̅̅̅
Prove: 𝐵𝐶 ≅ ̅̅̅̅
𝐷𝐶
Statements
1. ̅̅̅̅
𝐴𝐶 bisects ∠BAD
Reasons
1. ________________________
2.
2. Given
3. _____________________________
3. Definition of angle bisector
4. ̅̅̅̅
𝐴𝐶 ≅ ̅̅̅̅
𝐴𝐶
4.
5. ∆ACB ≅ ∆ACD
5. ____________________________
̅̅̅̅ ≅ ̅̅̅̅
6. 𝐵𝐶
𝐷𝐶
6. ____________________________
22. Given the information in the diagram, fill in the missing statements and reasons to show
that ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐸𝐷
Prove: ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐸𝐷
Statements
̅̅̅̅ ≅ ̅̅̅̅
1. 𝐵𝐶
𝐷𝐶
Reasons
1. ________________________
2.
2. Given
3. _____________________________
3. Right angles are congruent
4. ∠ACB ≅ ∠ECD
4.
5. ∆ABC ≅ ∆EDC
5. ____________________________
6. ̅̅̅̅
𝐴𝐵 ≅ ̅̅̅̅
𝐸𝐷
6. ____________________________
Sketch the overlapping triangles separately. Mark all congruent angles and sides. Then tell
the theorem or postulate you can use to show that ∆DCF ≅ ∆EFC.
23.
24.
Tell which triangles you need to show are congruent in order to show that the statement is
true.
25. ∠A ≅ ∠D
26. ∠J ≅ ∠N
27. ̅̅̅̅
𝐷𝐸 ≅ ̅̅̅̅
𝐵𝐴
∆________ ≅ ∆________
∆________ ≅ ∆________
∆________ ≅ ∆________
Fill in the blank.
28. If a point is on the angle bisector, then it is ___________________________ from the two sides
of the angle.
Use the information in the diagram to find the measure.
29.
30.
Write an equation and solve for x.
31.
32.
Equation:
x = _____
33.
Equation:
x = _____ PS = _____ RS = _____
Equation:
x = _____ PM = _____ MN = _____
34. If a point is on the perpendicular bisector of a segment, then it is __________________ from
the endpoints of the segment.
Use the information in the diagram to find the measure.
35.
36.
Write an equation and solve for x.
37.
38.
Equation:
39.
Equation:
x = _____ BC = _____ DC = _____
Equation:
x = _____ AB = _____ CB = _____
x = _____ AD = _____ CD = _____
̅̅̅ ?
40. What is the length of 𝐽𝐾
A. 6
B. 13
C. 18
D. 26
E. 36
Solve for x and y.
41.
42.
Equation to solve for x:
Equation to solve for y:
X = __________
y = _________
Equation to solve for x:
x = __________
Equation to solve for y:
y = ____________