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.
Find the value of each variable.
11.
12.
13.
14. The legs of an isosceles triangle have lengths of x  1 and 7  x . The base has length of
2x  4 .
A. Draw a picture to represent the situation.
B. Write and solve an equation to find the value of x.
C. What is the length of the base?
x  _______
base = _______
15. The measures of two of the sides of an equilateral triangle are 3x  15 inches and 7 x  5
inches.
A. Draw a picture to represent the situation.
B. Write and solve an equation to find the value of x.
C. What is the measure of the third side, in inches?
16. In GHI , HI  GH , mIHG  3x  4, and mIGH  2 x  24.
A. Draw a picture to represent the situation.
B. Write and solve an equation to find the value of x.
C. mHIG  _______
x  _______
3rd side = _______
Find the value of the variable.
17.
18.
x  _______
Complete the following proofs.
19.
Given: PX  PY ; MP bisects XPY
Prove: XM  MY
Statements
1.
2.
3.
4.
5.
6.
20.
Given: 3  4; AB  CD
Prove: 1  2
Statements
1.
2.
3.
4.
5.
6.
21.
Reasons
1.
2.
3.
4.
5.
6.
Reasons
1.
2.
3.
4.
5.
6.
Given: 1  2; 3  4
Prove: PQ  RQ
Statements
1.
2.
3.
4.
5.
Reasons
1.
2.
3.
4.
5.
Hint: You will need to use the large
triangle first. It will give you what you
need to find the smaller triangles
congruent to each other. Then use those
to find parts of the middle triangle! I
would recommend highlighting the
different sets of triangles!
22. Given: BD bisects ABC; BD  AC
Prove: AB  CB
Statements
Reasons
1.
2.
3.
4.
5.
6.
1.
2.
3.
4.
5.
6.
23. Given: XA  YA; XC  YC
Prove: XAC  YAC
Statements
Reasons
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
24. Given: NK bisects JNM ; NM  NK ; NL  NJ
Prove: JNK  LNM
Statements
Reasons
1.
2.
3.
4.
5.
1.
2.
3.
4.
5.
25. Given: BC AD; BC  AD
Prove: B  D
Statements
Reasons
1.
2.
3.
4.
5.
6.
1.
2.
3.
4.
5.
6.
For #26-27, a problem is given, followed by a student’s incorrect solution. Circle the
error(s) the student made in his/her solution. Then write the correct solution in the blanks
provided.
26.
Correct Solution:
Statements
Reasons
27.
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