1. 4-5 Warm Up Lesson Presentation Lesson Quiz
Triangle Congruence: ASA and AAS
Holt Geometry
Warm Up
Lesson Presentation
Lesson Quiz

2. Do Now
1. What are sides AC and BC called? Side AB?
2. Which side is in between A and C?
3. Given DEF and GHI, if D  G and E  H, why is F  I?

3. Objectives
Apply ASA and AAS to construct triangles and to solve problems.
Prove triangles congruent by using ASA and AAS.

4. Vocabulary
included side

5. An included side is the common side of two consecutive angles in a polygon. The following postulate uses the idea of an included side.

7. Example 1: Applying ASA Congruence
Determine if you can use ASA to prove the triangles congruent. Explain.

8. Example 2
Determine if you can use ASA to prove NKL  LMN. Explain.

10. Example 3: Using AAS to Prove Triangles Congruent
Use AAS to prove the triangles congruent.
Given: X  V, YZW  YWZ, XY  VY
Prove:  XYZ  VYW

11. Lesson Quiz: Part I
Identify the postulate or theorem that proves the triangles congruent, or determine “not possible.”
ASA
not possible
SAS or SSS

12. Congruence Postulates Extra Examples
SSS, ASA, SAS, AAS

13. 1. Given: ÐA @ÐD AB @ DE ÐB @ ÐE.
ASA

14. 2. Given: ÐE
DF.
AAS

15. 3. Given: ÐE
EF.
ASA

16. 4. Given: DF
EF.
SAS

17. 5. Given: ÐF
EF.
AAS

18. 6. Given: DE EF
DF.
SSS

19. 7. Given: ÐC and ÐF are rt. Ðs AB @ DE
ÐD.
AAS

20. 8. Given: ÐC and ÐF are rt. Ðs AC @ DF
ÐE.
AAS

21. 9. Given: ÐE
DF.
AAS

22. 10. Given: ÐC and ÐF are rt. ÐsÐE
EF.
ASA

23. 11. Given: DE
ÐE.
ASA

24. 12. Given: ÐF
EF.
AAS

25. 13. Given: BC ^ AC
EF ^ DF DE
ÐE.
AAS

26. 14. Given: DE EF
DF.
SSS

27. 15. Given: DF
EF.
SAS