Geometry
Chapter 4 Review
Name____________________________________
SAT   GRE. Complete each congruence statement.
1. S 
2. GR 
3. E 
4. AT 
5. ERG 
6. EG 
7. REG 
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.
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?
19. The measures of two of the sides of an equilateral triangle are 3x 15 inches and 7 x  5
inches. What is the measure of the third side, in inches?
20. In GHI , HI  GH , mIHG  3x  4, and mIGH  2 x  24. Draw and label a picture to
represent this situation. Then write and solve an equation to find the value of x. What is
mHIG ?
Find the missing angles.
21.
m  _______
n  _______
22.
x  _______
y  _______
Complete the following proofs.
23.
Given: PX  PY ; ZP bisects XY
Prove: PXZ  PYZ
(Hint: You will need to prove the smaller triangles congruent first!)
Statements
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8.
24.
Given: 3  4; AB  CD
Prove: 1  2
Statements
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6.
25.
Reasons
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6.
Given: LO  MN ; LO MN
Prove: MLN  ONL
Statements
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26.
Reasons
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Reasons
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6.
Given: 1  2; 3  4
Prove: PMQ  RMQ
Statements
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Reasons
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27.
Given: M is the midpoint of AB; MC  AC; MD  BD; 1  2
Prove: ACM  BDM
Statements
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Reasons
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28. Given: ADB  CDB; ABD  CBD
Prove: AB  CB
Statements
Reasons
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29. Given: XA  YA; XC  YC
Prove: XAC  YAC
Statements
Reasons
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30. Given: NK bisects JNM ; NM  NK ; NL  NJ
Prove: JNK  LNM
Statements
Reasons
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31. Given: BC AD; BC  AD
Prove: ABC  CDA
Statements
Reasons
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32. Given: QU  AD; QA  UD
Prove: 1  2
Statements
Reasons
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33. Given: PR  QS ; PS  QR
Prove: P  Q
Statements
Reasons
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34. Given: AD  AE; D  E
Prove: EB  CD
Statements
Reasons
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