Name _________________________________________
Period ____
GP
UNIT #4: TRIANGLE CONGRUENCE
Congruent Triangles
SSS
SAS
AAS
HL
ASA
Congruence
Statement
Reason
Corresponding Parts
Reflexive Property
Name __________________________ Period ______
Triangle Congruence
I. Name the congruent triangles.
1. OGD  ________
GH
RAC  ________
2.
C
R
A
3.
LIN  _______
I A
N
R
E
FOX  ______
4.
F
O
O
L
X
E
X
B
II. Name the congruent triangle and the congruent parts..
7.
FGH  ______
EFI 
FG  _____
_____
G
_____
GH  _____
H
_____
FH  _____
Use the congruency statement to fill in the corresponding congruent parts.
8. EFI  HGI
E
O
G
_____
FI  _____
FE  _____
FIE 
_____
EFI 
_____
IE  _____
9.
PQR  MNR . Find x.
ABC  ADC. Find y.
10.
Q
A
x°
R
(3y)°
M
21°
P
35o
N
D
C
Third Angles Theorem (add to Theorems, Postulates and Definitions Card) –
B
Triangle Congruence Worksheet #1
For each pair of triangles, tell which postulates, if any, make the triangles congruent.
12. ABC  EFD
13. ABC  CDA
______________
C
______________
C
B
D
A
F
A
B
D
E
14. ABC  EFD
15. ADC  BDC
______________
C
F
C
B
A
D
21. MAD  MBC
______________
A
E
ABE
______________
B
D
 CDE
______________
D
D
C
C
E
A
A
23. ACB  ADB
______________
C
B
A
D
23.
B
B
M
______________
23.
______________
Triangle Congruence Worksheet #2
I. For each pair of triangles, tell which postulate, if any, can be used to prove the triangles congruent.
1. AEB  DEC
2. CDE  ABF ______________
______________
A
D
E
C
F
C
B
E
A
B
D
3. DEA  BEC
A
4. AGE  CDF ______________
______________
B
E
D
C
5. RTS  CBA
6. ABC  ADC ______________
______________
B
T
S
C
A
C
R
A
7. BAP  BCP
Given: BD bisects
B
D
8. SAT  SAR ______________
______________
ABC
A
R
S
A
B
D
P
T
C
II. For each pair of triangles, tell: (a) Are they congruent (b) Write the triangle congruency statement.
(c) Give the postulate that makes them congruent.
1.
D
2.
C
3. Given: T is the midpoint of WR
O
A
E
T
E
L
A
E
R
W
V
B
a. ______________
a. ______________
a. ______________
b. _____   _____
b. _____   _____
b. _____   _____
c. ______________
c. ______________
c. ______________
4.
5. Given: IH Bisects WIS
6.
I
W
H
S
L
U
G
E
a. ______________
a. ______________
a. ______________
b. _____   _____
b. _____   _____
b. _____   _____
c. ______________
c. ______________
c. ______________
7.
8.
9.
H
P
A
T
M
a. ______________
a. ______________
a. ______________
b. _____   _____
b. _____   _____
b. _____   _____
c. ______________
c. ______________
c. ______________
10. Given: I is the midpoint
of ME and SL
M
11.
12.
C
F
L
I
S
E
B
A
D
E
a. ______________
a. ______________
a. ______________
b. _____   _____
b. _____   _____
b. _____   _____
c. ______________
c. ______________
c. ______________
III. Using the given postulate, tell which parts of the pair of triangles should be shown congruent.
1. SAS
2. ASA
3. SSS
C
A
E
D
B
F
F
B
A
B
A
E
D
C
C
D
_______  ________
4. AAS
________  ________
5. HL
_______  _______
6. ASA
P
P
D
S
C
T
R
A
Q
_______  ________
R
S
Q
________  ________
_______  _______
B
Name:
Period:
GH
Triangle Proofs Worksheet
For each problem below, write a two-column proof on a separate piece of paper.
I. Proving Triangles Congruent:
1.
5.
2.
3.
6.
4.
II. Using CPCTC
7.
10.
1
8.
9.
2
11.
Review: Triangles and Triangle Congruence
You will need a separate piece of paper to show all your work. This review is not comprehensive; always be sure
to go back through your old homework and quizzes.
C
 I can write a congruency statement representing two congruent polygons
O
G
1. Write a congruency statement for the two triangles at right.
R
A
E
 I can identify congruent parts of a polygon, given a congruency statement
2. List ALL of the congruent parts if
EFG  HGF
 I can use algebra to find the side lengths and angle measures of congruent polygons
3.
WXY  ZYX . Find p.
X
Y
2
2p
V
20
(7p+13
)
4.
ADC  CBA. Find x.
W
Z
D
C
(2x 2 + 7)°
1
2
(x 2 – 8x)°
A
B
 I can name the five ways to prove triangles are congruent
5.
Name the 5 ways to prove triangles congruent.
 I can prove triangles are congruent
For each pair of triangles, tell: (a) Are they congruent (b) Write the triangle congruency statement. (c) Give
the postulate that makes them congruent.
B
6.
8. Given: I is the midpoint
of ME and SL
A
C
M
L
I
D
7.
S
A
E
T
W
R
E
 I can mark pieces of a triangle congruent given how they are to be proved congruent
P
9. What information is
10.
What information
missing to use HL?
is missing to use
SAS?
C
D
R
S
Q
A
B
IV. For which value(s) of x are the triangles congruent?
3. x = _______________
A
4. x = _______________
A
B
m 3 = x2
m 4 = 7x - 10
7x - 4
4x + 8
1
3
E
2
4
C
D
C
B
R
W
5. x = _______________
A
Z
x2 + 2x
x2 + 24
x2 + 3x
B
D
C
9x - 8
R
 I can write a two-column proof over congruent triangles
11.
12. Complete and review ALL proofs on the proofs worksheet.
S
T