Download Congruence by SSS and SAS

Name: _________________________________
Congruent Figures Worksheet
C
1) ΔABC  ΔDEF.
D
F
E
A
B
a) Name 3 pairs of congruent sides:
b) Name 3 pairs of congruent angles:
___________ ___________ ___________
___________ ___________ ___________
c) mA=70, what is the measure of D? ____
2) Quadrilateral ABCD  Quadrilateral QRST.
AB = 12, BC = 13, CD = 15, AD = 17.
a) What angle is congruent to CDA? _______
b) What side is congruent to RS ? __________
c) Find TQ. ______
d) Find perimeter of QRST. _______
D
3) Pentagons ABCDE and PQRST are congruent.
If the length of DE is (3x - 4) inches, and the length of ST
is (2x + 8) inches. What is the length of DE?
C
E
P
B
N
Y
B
V
X
A
C
Q
T
A
4) Write a congruence statement for each pair of triangles
R
S
55o
55o
Z
M
P
Q
U
5)  ABC   DEF.


DF = _______
C
D
AB = _______
F
42
A = _______ D = _______
5
E = _______ F = _______
A
3
67
B
6
E
6) You make a photocopy of a picture. Are the original and the copy congruent?
You make another photocopy, but set the machine to reduce the image by 20%. Are the original
and the copy congruent? Why?
7) DB is both the perpendicular bisector of AC and an angle bisector ADC.


D
A
B
C
Considering  ABD and  CBD, state all pairs of congruent sides and congruent angles, and explain why
each pair is congruent. Do you have enough information to state that the triangles are congruent?


Name: _________________________________
Congruence by SSS Worksheet
1) For each, name all pairs of congruent parts.
a)
E is the midpoint of CD
E
A
b) CD bisects AB at E
B


E
A

c) AB and CD bisect each
other at E
D
B

C
d) DB is a median

2) Given:
Prove:
BD bisects AC
AB  CB
ADB  CDB
Statement
Reason
1. BD bisects AC
1.
2.
2.
AD  DC
3. AB  CB
3.
4. BD  BD
4.
5. ADB  CDB
5.
B
e) DB is an angle bisector

For #2-4, fill in the missing statements or reasons:
D
C
e) DB is a perpendicular bisector

E
A

S
3) Given: PQ  PS
QR  SR
Prove: PSR  PQR
R
P
Q
Statement
1.
Reason
Given
2.
Given
3.
reflexive property of equality
4.
SSS
4) Given:
D
DB is a median
AD  DC
Prove:

ΔABD  ΔCBD
A
B
C

Statement
Reason
1.
1. Given
2.
2. Given
3.
3. A median is a segment in a triangle from a
vertex to the midpoint of the opposite side.
4.
4. A midpoint divides a segments into 2 congruent segments
5.
5. Reflexive property of equality
6.
6. SSS
Name: _________________________________
Congruence by SAS Worksheet
1) Given: ABE intersects CBD at B
B is the midpoint of CD
B s the midpoint of AE

EBD
Prove:  ABC  

Statement




1. ABE intersects CBD at B

B
A
Reason
1.
2. B is the midpoint of CD

2.
3. B s the midpoint of AE

3.
4. AB  BE
4.

5. CB  BD
5.
6. CBA  DBE
6.
7.  ABC   EBD
7.




E
C
 
2) Given: WY bisects ZWX
WZ  WX
Prove: WYZ  WYX
Statement
Reason
1. WY bisects ZWX
1.
2. ZWY  XWY
2.
3. WZ  WX
3.
4. WY  WY
4.
5. WYZ  WYX
5.
D
3) Given:
Prove:
RU  TU
SU  RT
RSU  TSU
Statement
1.
S
Reason
1. Given
2.
2. Given
3. RUS and TUS are
right angles
3.
4. RUS  TUS
4.
5. SU  SU
5.
6. RSU  TSU
6
R
T
U
On Your Own !
Hint - a congruent pair of alternate interior angles will help you complete this proof.
4) Given:
Prove:



Statement
MN // QP
MN  QP
 MNQ   PQN

Q
M
 
Reason
.
P
N
SAS & SSS Congruence Worksheet
Name: _________________________________
Can the following pairs of triangles be proven to be congruent? If so, state the postulate used
otherwise state “cannot be proven”.
1)
2)
3)
4)
5). Given:
Prove:

U
SU bisects RST
RS  ST
 RSU   TSU

Statement

 

Reason
T
R
S
6)
Given:
Prove:
C
D
ABCD is a square
 ABC   CDA
 

Statement
Reason
A
.
B
Y
7) Hint - use the isosceles triangle theorem.
Given: W  X
YZ is a median
Prove:  WZY   XZY

Statement
Reason

 

.
W
Z
X
Name: _________________________________
ASA & AAS Congruence Worksheet
For #1-4, state whether the ASA Postulate or the AAS Theorem can be applied directly to prove the
triangles congruent. If the triangles cannot be proved congruent, write ‘not possible’.
1)
2)
3)
4)
5) Given: Q  S
TRS  RTQ
Prove: QRT  STR

Statement

1.

Reason
1. Given
2.
2. Given
3.
3. Reflexive property of equality
4
4. AAS
6) Given: N is the midpoint of LP
L  P
Prove: LNM  PNQ

Statement


Reason
B
7. Given: BC is an altitude of ABD
BC bisects ABD
Prove: ACB  DCB
Statement
Reason
A
C
D
Mixed Practice Worksheet
Name: _________________________________
D
E
1) Given: AD // BE
B is the midpoint of AC
ABD  BCE
Prove: ABD  CBE
A
Statement
C
B
Reason
D
2) Given: EB  FD
F
E is the midpoint of AB
F is the midpoint of DC

DE  FB
DA  BC 
Prove: AED  CFB


Statement

A
Reason
E
B
C