4.5

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4.5 Prove Triangles Congruent by ASA and AAS

• Geometry
• Ms. Rinaldi

2
Angle-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
3
EXAMPLE 1
Use ASA
Decide whether the congruence statement is true.
Explain your reasoning.
SOLUTION
(A) (S) (A)
So, by ASA,
4
EXAMPLE 2
Use ASA
Decide whether the congruence statement is true.
Explain your reasoning.
5
Angle-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
6
EXAMPLE 3
Use AAS
Decide whether the congruence statement is true.
Explain your reasoning.
SOLUTION
(A) (A) (S)
So, by AAS,
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EXAMPLE 4
Use AAS
Decide whether the congruence statement is true.
Explain your reasoning.
8
EXAMPLE 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
9
EXAMPLE 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
10
EXAMPLE 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