Proving Triangles are Congruent ASA and AAS

1
Proving Triangles are CongruentASA and AAS

• Chapter 4.5
• Objectives To use the ASA and AAS Theorem to
  prove that triangles are congruent

2
ASA ? ? Theorem

• If two angles and the included side of one
  triangle, are congruent to the corresponding
  angles and side in a second triangle, then the
  triangles are congruent.

3
?ABC ? ?XYZ Why?
ASA ? ? Theorem
4
Use ASA in Proofs
Write a two-column proof.
5
Step
Reason
Given
Def of Midpt.
Given
?W ? ?E
Alternate Int. ? Thm.
?RLW ? ?DLE
Vertical ? Thm.
?WRL ? ?EDL
ASA ? ? Thm.
6
Write a two-column proof.
7
Step
Reason
Given
?CBD ? ?ADB
Alternate Int. ? Thm.
?CDB ? ?ABD
Alternate Int. ? Thm.
Reflexive Property
?ABD ? ?CDB
ASA ? ? Theorem.
8
AAS ? ? Theorem

• If two angles and a non-included side of one
  triangle, are congruent to the corresponding
  angles and side in a second triangle, then the
  triangles are congruent.

9
?ABC ? ?XYZ Why?
AAS ? ? Theorem
10
Write a two-column proof.
?JNM ? ?KNL
11
IMPORTANT HINT When you are given overlapping
triangles, draw them separately.
12
Step
Reason
?NKL ? ?NJM
Given
Given
Reflexive Property
?JNM ? ?KN L
?JNM ? ?KNL
AAS ? ? Thm.
13
Homework

• Chapter 4-5
• Pg 238
• 1-4, 8, 9, 15, 27
• These are all
• two-column proofs!!!

Video B 740-
Interactive Lab Proofs and Congruent Triangles