5'3 Proving Triangles are Congruent: ASA and AAS

1
5.3 Proving Triangles are Congruent ASA and AAS

• Angle Side Angle Congruence Postulate (ASA)
• 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 A D, and
• Side AC DF, and
• Angle C F, then
• ABC DEF.

B


C
A

E

F
D
2
Determine When to Use ASA Congruence

• Based on the diagram, can you use the ASA
  Congruence Postulate to show that the triangles
  are congruent? Explain your reasoning.
• a.
• Solution
• You are given that C F, B
  F, and BC FE.
• You can use the ASA Congruence Postulate to show
  that
• ABC DEF.

B
E
D
A
A
C
F



3

• Based on the diagram, can you use the ASA
  Congruence Postulate to show that the triangles
  are congruent? Explain your reasoning.
• b.
• Solution
• You are given that R Y and S
  X.
• You know that RT YZ, but these sides are not
  included between the congruent angles, so you
  cannot use the ASA Congruence Postulate.

T
Z
X
Y
R
S


4
Angle Angle Side Congruence Theorem (AAS)

• If two angles and a non-included side of one
  triangle are congruent to two angles and the
  corresponding non-included side of a second
  triangle, then the two triangles are congruent.
• If Angle A D, and
• Angle C F, and
• Side BC EF, then
• ABC DEF

B


A
C

E
F
D
5
Determine What Information is Missing

• What additional congruence is needed to show that
  JKL NML by the AAS Congruence Theorem?
• Solution
• You are given KL ML.
• Because KLJ and MLN are vertical angles,
• KLJ MLN.
• The angles that make KL and ML the non-included
  sides are J and N, so you need to know
  that J N.

N
K
L

M
J


6
More Practice!!!

• Textbook p. 253 1 9, p. 254 10 22 -
  finish for homework