If two angles and a non-included side of one triangle are congruent to the corresponding two angles and a non-included side of another triangle, then the triangles are congruent.

1. Elton John B. Embodo

2. a) identify whether triangles are congruent through AAS Congruence
theorem or not;
b) Complete the proof for congruent triangles through AAS
Congruence Theorem;
c) Prove that the triangles are congruent through AAS congruence
theorem.

3. Given: and are right angles
Prove:
Proof:
P N
1 3  
1 2
4
3
M N
OP
MNO OPM  
Statement Reason
1. and are right angles
2.
3.
4.
5.
P N
P N  
1 3  
MO MO
MNO OPM  

4. Given: and are right angles
Prove:
Proof:
P N
1 3  
1 2
4
M N
OP
MNO OPM  
Statement Reason
1. and are right
angles
2.
3.
4.
5.
P N
P N  
1 3  
MO MO
MNO OPM  
Given
All right angles are congruent.
Given
Re flexivity
AAS Congruence Theorem
3

5. If two angles anda non-includedsideof one triangleare
congruent to the correspondingtwo anglesand a non-
includedsideof another triangle, then the two trianglesare
congruent.
and then,
P
O
Q
T
U S
,O S Q U     
PQ UT
OPQ STU  

6. Directions: Completetheproof for congruent trianglesthroughAAS
CongruenceTheorem by putting additionalcongruent parts on the
figures. Copy the figuresand list thecongruentparts of both
triangles.
1.
2.
M
R
O S
T
Q
K
E
S
Q
U

7. 3.
4. 5.
S
V
T
U
O
N P
M
S
U V
T

8. DIRECTIONS: Prove thatthe two triangles below are congruent
throughAAS CongruenceTheorem.List 3 statementswith
corresponding reasons. Use ½ sheet of paper crosswise.
bisects at
Prove that
C
L
A
B
M
BL CM A
L B  
CAL BAM  