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Geometry A
Chapter 4 Review
Section 4-2
Section 4-1
In Problems 1 and 2, quadrilateral WASH
quadrilateral NOTE.
1. List (all 8) corresponding parts.
1. In VGB , which sides include B ?
2. In STN , which angle is included between
NS and TN ?
2. m O  m T  90 and m H  36 .
Find m N .
3. Which triangles can you prove congruent?
Tell whether you would use the SSS or SAS
Postulate.
Y
A
3. Write a statement of triangle congruence.
P
X
P
Z
F
B
D
H
4. What other information do you need to
prove DWO  DWG ?
R
D
4. Write a statement of triangle congruence.
B
A
1 2
W
O
C
G
D
5. Explain your reasoning in Problem 4 above.
5. Can you prove SED  BUT from the
information given? Explain. U
D
T
E
S
B
A
3.
Additional Examples
1. Suppose that F is congruent to C and
I is NOT congruent to C . Name the
triangles that are congruent by the ASA
Postulate.
D
O
C
T
G
A
2
D
F
C
Given: B  D , AB || CD
Prove: ABC  CDA
I
N
A
Y
2.
X
B
1
P
B
Given: A  B , AP  BP
Prove: APX  BPY
P
O
4.
Q
S
1 2
R
Given: S  Q , RP bisects SRQ
Prove: SRP  QRP
CLOSURE
Explain why the letters of ASA and AAS are
written in a different order.
Section 4-3
1. Which side is included between R and
F in FTR ?
Section 4-4
1. What does “CPCTC” stand for?
Use the diagram for Problems 2 and 3.
A
2. Which angles in STU include US ?
C
B
M
Tell whether you can prove the triangles
congruent by ASA or AAS. If you can, state a
triangle congruence and the postulate or
theorem you used. If not, write NOT
POSSIBLE.
3.
G
2. Tell how you would show ABM  ACM .
P
H
I
Q
R
3. Tell what other parts are congruent by
CPCTC.
L
P
4.
Use the diagram for Problems 4 and 5.
Y
S
A
R
U
T
Q
A
4. Tell how you would show RUQ  TUS .
5.
B
X
C
5. Tell what other parts are congruent by
CPCTC.
Section 4-5
Use the diagram for Problems 1-3.
Section 4-6
For Problems 1 and 2, tell whether the HL
Theorem can be used to prove the triangles
congruent. If so, explain. If no, write NOT
POSSIBLE.
1. A
A
B
B
C
M
C
1. If m BAC  38 , find m C .
R
D
2. If m BAM  m CAM  23 , find
m BMA.
Q
2.
E
T
W
3. If m B  3 x and m BAC  2 x  20 ,
find x .
For Problems 3 and 4, what additional
information do you need to prove the triangles
congruent by the HL Theorem?
3. LMX  LOX
4. Find the values of x and y.
M
L
X
60
18
60
O
N
y
60
x
5. ABCDEF is a regular hexagon.
Find m BAC .
A
4. AMD  CNB
B
N
A
C
F
D
E
D
M
C
B
Section 4-7
1. Identify any common sides and angles in
AXY and BYX .
A
REVIEW PROBLEMS
1. Given: AB  BC ; DC  BC ; 1  2
Prove: AC  DB
A
D
X
E
Y
2
1
B
C
B
For Problems 2 and 3, name a pair of
congruent overlapping triangles. State the
theorem or postulate that proves them
congruent.
2.
K
M
T
S
R
M
P
2.
3
H
G
R
4
3.
J
J
I
A
4.
Given: PK and JM bisect each other at R.
Prove: PJ  MK
B
X
D
1
K
2
Given: AC  BD , AD  BC
Prove: XD  XC
I
3. Given: KRM  PRO , KR  PR
Prove: RM  RO
R
K
4.
2
M
E
A
3
B
1
4
O
D
5
6
C
Given: 3  6 ; 3 is comp. 4 ;
6 is comp. 5
Prove: EBC is isosceles
C