Title: 4.5
14.5 Prove Triangles Congruent by ASA and AAS
2Angle-Side-Angle (ASA) Congruence Postulate
B
- If two angles and the included side of one
triangle are congruent to two angles and the
included side of a second triangle, then the two
triangles are congruent. - If Angle
- Side
- Angle
- Then
C
A
S
T
R
3EXAMPLE 1
Use ASA
Decide whether the congruence statement is true.
Explain your reasoning.
SOLUTION
(A) (S) (A)
So, by ASA,
4EXAMPLE 2
Use ASA
Decide whether the congruence statement is true.
Explain your reasoning.
5Angle-Angle-Side (AAS) Congruence Postulate
B
- If two angles and the non-included side of one
triangle are congruent to two angles and the
non-included side of a second triangle, then the
two triangles are congruent. - If Angle
- Angle
- Side
- Then
C
A
S
T
R
6EXAMPLE 3
Use AAS
Decide whether the congruence statement is true.
Explain your reasoning.
SOLUTION
(A) (A) (S)
So, by AAS,
7EXAMPLE 4
Use AAS
Decide whether the congruence statement is true.
Explain your reasoning.
8EXAMPLE 5
Use ASA or AAS
State the third congruence that must be given to
prove that using the indicated postulate.
B
E
Given Use the ASA Congruence Postulate.
C
A
F
D
9EXAMPLE 6
Use ASA or AAS
State the third congruence that must be given to
prove that using the indicated postulate.
B
E
Given Use the ASA Congruence Postulate.
C
A
F
D
10EXAMPLE 7
Use ASA or AAS
State the third congruence that must be given to
prove that using the indicated postulate.
B
E
Given Use the AAS Congruence Postulate.
C
A
F
D