1. Triangle Congruence by ASA and AAS
Geometry 4-3

2. An “Included Side” is the side that is directly between two angles
Included Sides

3. Which side in the following triangle is the “included side”?B A
Included Sides

4. Which side in the following triangle is the “included side”?B A
Included Sides

5. Which side in the following triangle is the “included side”?B
Included Sides

6. Which side in the following triangle is the “included side”?B
Included Sides

7. Investigating ASA Get your supplies ready Ruler Marker or pencil
Two sheets of Patty Paper
Investigating ASA

8. Draw a triangle on one sheet of Patty Paper
Investigating ASA

9. Pick and mark two angles of the triangleB
Investigating ASA

10. Investigating ASA Copy the marked angle and the two adjacent sides
Cut them out, the sides can be any length
Investigating ASA

11. Investigating ASA Using the Angle – Side - Angle that you cut out
Can you form any triangle that is NOT congruent to the original triangle?
Investigating ASA

12. Is it possible to form a new triangle that is NOT congruent to your original triangle?
This is called Angle-Side-Angle congruence
Investigating ASA

13. ASA Congruence

14. AAS
Triangle Congruence

15. An “Non-Included Side” is the side that is Adjacent to two angles
Non-Included Sides

16. Identify The Congruency
Describe the following triangle congruence
AAS B A
Identify The Congruency

17. Identify The Congruency
Describe the following triangle congruence
ASA A B
Identify The Congruency

18. Identify The Congruency
Describe the following triangle congruence
AAS A B
Identify The Congruency

19. Identify The Congruency
Describe the following triangle congruence
SAS A
Identify The Congruency

20. Identify The Congruency
Describe the following triangle congruence
SAS A
Identify The Congruency

21. Identify The Congruency
Describe the following triangle congruence
ASA A B
Identify The Congruency

22. Identify The Congruency
Describe the following triangle congruence
ASA B A
Identify The Congruency

23. Identify The Congruency
Describe the following triangle congruence
AAS A B
Identify The Congruency

24. Identify The Congruency
Describe the following triangle congruence
AAS B A
Identify The Congruency

25. Identify The Congruency
Describe the following triangle congruence A
AAS B
Identify The Congruency

26. Identify The Congruency
Describe the following triangle congruence
SAS A
Identify The Congruency

27. Identify The Congruency
Describe the following triangle congruence
AAA B A C
Identify The Congruency

28. Identify The Congruency
Describe the following triangle congruence
AAS B A
Identify The Congruency

29. Investigating AAS Get your supplies ready Ruler Marker or pencil
Two sheets of Patty Paper
Scissors
Investigating AAS

30. Draw a triangle on one sheet of Patty Paper
Investigating AAS

31. Pick and mark two angles of the triangleB
Investigating AAS

32. Mark an adjacent side A B
Investigating AAS

33. Copy the marked side, and its adjacent angle only onto a piece of patty paper
Cut it out
Investigating AAS

34. Copy the OTHER angle onto a piece of patty paper, cut it out
Investigating AAS

35. Investigating AAS Using the Angle – Angle - Side that you cut out
Can you form any triangle that is NOT congruent to the original triangle?
Investigating AAS

36. AAS Congruence

37. Side Side Side congruence
2. Side Angle Side congruence

38. Angle T
Angle C
Angle S
Angle G

39. 5. SSS Congruence
6. Not enough information given

41. ∠𝐶≅∠𝐹

44. Yes, SAS Congruence

45. Yes, ASA Congruence

46. Yes, SAS Congruence

47. Yes, SSS Congruence

48. Yes, SAS Congruence

49. Yes, SAS Congruence

50. Yes, AAS

51. Yes, AAS

56. Pages 197 – 200
9 – 18, 29, 32
Homework