1. Proving Triangles are Congruent ASA 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? B C A X Z Y
ASA   Theorem

4. Use ASA in Proofs
Write a two-column proof.

5. Step
Reason
L is the midpoint of WE
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? B C A X Z Y
AAS   Theorem

10. Write a two-column proof.
JNM  KNL

11. J N M L N K IMPORTANT HINT:
When you are given overlapping triangles, draw them separately.

12. K J L M N N Step Reason NKL  NJM Given Given JNM  KN L
Reflexive Property
JNM  KNL
AAS   Thm.

13. Interactive Lab: Proofs and Congruent Triangles
Homework
Chapter 4-5
Pg 238
1-4, 8, 9, 15, 27
These are all
two-column proofs!!!
Video B
7:40-
Interactive Lab: Proofs and Congruent Triangles