4.5

1
4.5 Prove Triangles Congruent by ASA and AAS

• In a polygon, the side connecting the vertices of
  two angles is the included side. Given two angle
  measures and the length of the included side, you
  can only make one triangle. So, all triangles
  with those measurements are congruent.

2
4.5 Prove Triangles Congruent by ASA and AAS
3
4.5 Prove Triangles Congruent by ASA and AAS
4
4.5 Prove Triangles Congruent by ASA and AAS

• Can the triangles be proven congruent with the
  information given in the diagram? If so, state
  the postulate or theorem you would use

5
4.5 Prove Triangles Congruent by ASA and AAS
6
EXAMPLE 1
Use ASA
Decide whether the congruence statement is true.
Explain your reasoning.
SOLUTION
(A) (S) (A)
So, by ASA,
7
EXAMPLE 2
Use ASA
Decide whether the congruence statement is true.
Explain your reasoning.
8
EXAMPLE 3
Use AAS
Decide whether the congruence statement is true.
Explain your reasoning.
SOLUTION
(A) (A) (S)
So, by AAS,
9
EXAMPLE 4
Use AAS
Decide whether the congruence statement is true.
Explain your reasoning.
10
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
11
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
12
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
13
4.5 Prove Triangles Congruent by ASA and AAS

• Write a proof.

14
4.5 Prove Triangles Congruent by ASA and AAS

• Write a proof.