This document outlines the AAS (Angle-Angle-Side) congruence theorem for determining triangle congruence. It provides specific steps to complete proofs for congruent triangles and instructions to illustrate the congruence through specified angles and sides. Additionally, it includes given conditions and expected proofs to validate conclusions about triangle congruence.

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  