Triangle Congruence
Name __________________________
Name the 5 postulates that can be used to prove a pair of triangles are congruent:_______, ______, _______, ______, _______
Determine which postulate, if any, will make a pair of triangles congruent, then list the congruent triangles properly.
If there is not enough information to make the triangles congruent, write NEI in the blanks.
_______proves ABC  ________
1.
C
2. _______proves ABC  _______
F
C
3. _______proves ADM  ______
D
C
F
A
B D
B
A
E
4. _______proves AFB  ________
D
E
5. _______proves BEC  _______
A
D
A
B
M
6. _______proves ELU  ______
B
L
U
G
E
C
F
E
E
A
B
D
7. _______proves ABC  ________
C
8. _______proves ADC  _______
9. _______proves ABE  ______
C
C
D
E
B
A
C
A
B
D
A
B
D
10. _______proves ABC  ________
T
11. _______proves AEB  _______
D
S
12. _______proves PNM  ______
C
C
E
R
A
B
A
13. _______proves ABP  ________
B
14. _______proves ATS  _______
A
R
B
D
P
S
A
T
C
15. _______proves TRU  ______
Triangle Proofs Worksheet
Name_____________________________________
For each problem below, write a two-column proof
1.
2.
3.
4.
6.
5.
7.
5.
8.
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
1. Write a congruency statement for the two triangles at right.
O
G
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.
W
ADC  CBA. Find x.
Z
D
C
(2x + 7)°
1
 I can name the five ways to prove triangles are congruent
5. Name the 5 ways to prove triangles congruent.
2
(x – 8x)°
A
B
 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
A
of ME and SL
C
M
7.
A
E
T
W
L
I
D
R
S
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
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.
O
1.
2.
3. Given: T is the midpoint of WR
D
C
A
E
E
E
L
A
a. ______________
B
T
V
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. ______________
8.
9.
7.
R
W
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
112.
C
F
L
I
S
E
a. ______________
a. ______________
B
A
D
a. ______________
b. _____   _____
b. _____   _____
b. _____   _____
c. ______________
c. ______________
c. ______________
E
III.
1.
Using the given postulate, tell which parts of the pair of triangles should be shown congruent.
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