Download 4.4 Proving Triangles are Congruent: ASA and AAS

4.4 Proving Triangles are
Congruent: ASA and
AAS
Geometry
Objectives:
1. Prove that triangles are congruent
using the ASA Congruence Postulate
and the AAS Congruence Theorem
2. Use congruence postulates and
theorems in real-life problems.
Postulate 21: Angle-Side-Angle
(ASA) Congruence Postulate
• If two angles and the
B
included side of one
triangle are
congruent to two
angles and the
C
included side of a
second triangle, then
the triangles are
congruent.
A
E
F
D
Theorem 6.1
• If two angles of one triangle are
congruent to two angles of another
triangle, then the third pair of angles are
congruent.
Theorem 4.5: Angle-Angle-Side
(AAS) Congruence Theorem
• If two angles and a
B
non-included side of
one triangle are
congruent to two
angles and the
corresponding non- C
included side of a
second triangle, then
the triangles are
congruent.
A
E
F
D
Theorem 4.5: Angle-Angle-Side
(AAS) Congruence Theorem
Given: A  D, C
 F, BC  EF
Prove: ∆ABC  ∆DEF
B
A
E
C
F
D