PDF GR 3. E 4. - Twinsburg City School District

[Pages:5]Honors Geometry Chapter 4 Review

Name____________________________________

SAT GRE. Complete each congruence statement.

1. S

2. GR

3. E 5. ERG 7. REG

4. AT 6. EG 8. R

9. Write a congruence statement. Identify all pairs of congruent corresponding parts.

Congruence Statement

_______________

Corresponding Sides

_______________

_______________

_______________

Corresponding Angles

_______________

_______________

_______________

10.

Can you prove the two triangles congruent? If so, write the congruence statement and name the postulate you would use. If not, write not possible and tell what other information you would need.

11.

12.

13.

14.

Find the value of each variable.

15.

16.

17.

18. The legs of an isosceles triangle have lengths of x 1 and 7 x . The base has length of 2x 4 . What is the length of the base?

Complete the following proofs.

19. Given: PX PY; ZP bisects XY Prove: PXZ PYZ

(Hint: You will need to prove the smaller triangles congruent first!)

Statements 1. 2. 3. 4. 5. 6. 7. 8.

Reasons 1. 2. 3. 4. 5. 6. 7. 8.

20. Given: 3 4; AB CD Prove: 1 2

Statements 1. 2. 3. 4. 5. 6.

Reasons 1. 2. 3. 4. 5. 6.

21. Given: LO MN; LO MN Prove: MLN ONL

Statements 1. 2. 3. 4. 5. 6.

Reasons 1. 2. 3. 4. 5. 6.

Given: 1 2;3 4 22.

Prove: PMQ RMQ

Statements 1. 2. 3. 4. 5. 6. 7.

Reasons 1. 2. 3. 4. 5. 6. 7.

23. Given: M is the midpoint of AB; MC AC; MD BD;1 2 Prove: ACM BDM

Statements 1. 2. 3. 4. 5. 6. 7.

Reasons 1. 2. 3. 4. 5. 6. 7.

24. The longest leg of ABC, AC , measures 10 centimeters. BC measures 8 centimeters. You measure two of the legs of XYZ and find that AC XZ and BC YZ . Can you conclude that two triangles to be congruent by the HL Theorem? Explain why or why not.

25. Given: ADB CDB; ABD CBD

Prove: AB CB

Statements

1. 2. 3. 4. 5.

Reasons

1. 2. 3. 4. 5.

26. Given: XA YA; XC YC

Prove: XAC YAC

Statements

1. 2. 3. 4. 5.

Reasons

1. 2. 3. 4. 5.

27. Given: NK bisects JNM; NM NK; NL NJ

Prove: JNK LNM

Statements

1. 2. 3. 4. 5.

Reasons

1. 2. 3. 4. 5.

28. Given: BC AD; BC AD

Prove: ABC CDA

Statements

1. 2. 3. 4. 5.

Reasons

1. 2. 3. 4. 5.

29. Given: QU AD; QA UD

Prove: 1 2

Statements

1. 2. 3. 4. 5.

30. Given: PR QS; PS QR

Prove: P Q

Statements

1. 2. 3. 4. 5.

31. Given: AD AE; D E

Prove: EB CD

Statements

1. 2. 3. 4. 5.

Reasons 1. 2. 3. 4. 5.

Reasons 1. 2. 3. 4. 5.

Reasons 1. 2. 3. 4. 5.

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