Geometry
Study Guides – retests for chapters 4, 5, and 7
Name_________________________
Chapter 4 – congruent triangles
Questions 1 – 2: Find the value of x and then classify the triangle by its angles.
1.
2.
x = __________
x = __________
classify – ____________________
classify – ____________________
Questions 3 – 4: Find the value of each variable.
3.
4.
x = __________
x = __________
y = __________
Questions 5 – 10: In the diagram, QRS  XYZ. Complete each statement.
5. mX = __________
6. mY = __________
7. mS = __________
8. XY = __________
9. RS  __________
10. YXZ  __________
H
11. Complete the following proof.
2
G
GIVEN:
GH  EF
GF  EH
E
1
PROVE:
1  2
F
Statements
Reasons
1. GH  EF
1.
2. GF  EH
2.
3. FH  FH
3.
4. FGH  HEF
4.
5. 1  2
5.
Possible Reasons
Given
Given
Prove
Definition of congruent sides
Reflexive property
Symmetric property
SSS
HL
ASA
Corresponding parts of   's are 
Questions 12 – 17: Is it possible to prove that the triangles are congruent? Circle YES
or NO!! If so, state the postulate or theorem you would use.
12.
13.
14.
Yes / No
Yes / No
Yes / No
Reason – ____________
Reason – ____________
Reason – ____________
15.
16.
Yes / No
Yes / No
Yes / No
Reason – ____________
Reason – ____________
Reason – ____________
17.
Chapter 5 – relationships in triangles
Questions 1 – 2: List the sides and angles in order from smallest to largest.
1.
2.
3. Which of the following could represent the side lengths of a triangle? Check all that apply.
4. The lengths of two sides of a triangle are 26 meters and 48 meters. What is the range of possible
lengths for the third side of this triangle? Write your answers in the boxes.
Questions 5 – 7: Use the triangle to the right to answer each question. All questions are
independent of each other.
5. If DE = 8x + 12 and KL = 10x – 9, what is DE?
6. If JL = 7x – 6 and EF = 9x + 8, what is EK?
7. If DF = 18x – 6 and JK = 3x + 11, what is JK?
Questions 8 – 9: Complete each statement with <, >, or =.
8.
AB __________ BC
9.
RS __________ VW
Questions 10 – 11: Find the length of each segment.
10. Find LK.
11. Find JK.
Questions 12 – 13: Find the value of x.
12.
13.
Questions 14 – 15: DE is the midsegment of ABC. Find the value of each variable.
14. Find the value of x.
15. Find the value of y.
16. Use the diagram to write and solve an inequality that describes the possible values of x.
Chapter 7 – right triangles
Questions 1 – 2: Find the value of x.
1.
2.
Questions 3 – 4: Given the three side lengths of a triangle, classify it as right, acute, or obtuse.
3.
5, 13, 12
4.
7, 26, 24
5. Find the value of x.
x
25
6. You are standing 350 feet away from a skyscraper that is 750 feet tall, as shown in the sketch. What
is the angle of elevation from you to the top of the building?
Questions 7 – 8: Find the value of each variable.
7.
8.
9. Find the value of a.
10. Ski lift cables are strung to the top of a 1200-foot mountain. The angle of elevation of the cables is
30°. How long are the cables?
Questions 11 – 13: Solve the right triangle by finding the missing pieces.
11. Find AC.
A
12. Find mA.
C
13. Find mB.
B