1. Triangle Congruence by ASA and AAS
February 27, 2012

2. Warm-up
Practice 4-2: Workbook p. 42, #1-15

3. Warm-up

4. Warm-up

5. Questions on Homework?

6. Questions on Homework?
#33:
Statements Reasons

7. Questions on Homework? 41.Prove ΔFGK ≅ ΔKLF 42. Prove ΔACB ≅ ΔECD
and bisect each other
43. Prove ΔGJK ≅ ΔGMK
bisects ∠JGM
44. Prove ΔAMC ≅ ΔMBD
┴ ; ┴ ; M is midpoint of

8. Section 4-3 Triangle Congruence by ASA and AAS
Objectives: Today you will learn to
prove triangles congruent using the ASA Postulate and AAS Theorem
Remember: Quiz on Wednesday on
4-1, 4-2, and 4-3

9. Investigation Congruence Applet:
Each Triangle Congruence Postulate uses three elements (sides and angles) to prove congruence.
Today let’s investigate using Angles (2 or 3) and/or one Side

10. Conclusions Angle-Side-Angle (ASA) Postulate
In which configuration(s) were the triangles always congruent?
Angle-Side-Angle (ASA) Postulate
Angle-Angle-Side (AAS) Theorem
In which configuration(s) were the triangles sometimes congruent?
Angle-Angle-Angle (AAA) – can’t use!

11. Angle-Side-Angle (ASA) Postulate
If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two
triangles are congruent.
ΔTUV ≅ ΔWXY

12. Angle-Angle-Side (AAS) Theorem
If two angles and a nonincluded side of one triangle are congruent to two angles and the corresponding nonincluded side of another triangle, then the triangles are congruent.
ΔABC ≅ ΔDEF

13. Angle-Angle-Side (AAS) Theorem
Proof:
∠C ≅ ∠F Given
∠B and ∠E are right ∠’s Given
∠B ≅ ∠E Rt ∠’s ≅
∠A ≅ ∠D Thm 4.1
ΔABC ≅ ΔDEF ASA Postulate
ΔABC ≅ ΔDEF

14. SSS Postulate SAS Postulate ASA Postulate AAS Theorem
Four Ways to Prove Δ’s ≅
SSS Postulate
SAS Postulate
ASA Postulate
AAS Theorem

15. Which Postulate/Thm? (if possible) and write Congruency Statement

16. Example 1: Prove: ΔAXP ≅ ΔBYP
Given: ≅ segments and angles as marked

17. Example 2: Prove ΔABC ≅ ΔCDA
Given: ≅ angles and || segments as marked

18. Example 3: Prove ΔABE ≅ ΔCDE

19. Example 4: Prove ΔJKL ≅ ΔPML

20. Example 5: Prove ΔQRT ≅ ΔSTR

21. Example 6: Find the values for x and y
Given: ΔABD ≅ ΔACD

22. Example 7: Find the values for x and y
Given: ΔABD ≅ ΔACD
If BC = 6, BD = ____
If m∠C = 55, m∠B = _____
and m∠BAC = _____
If m∠BAD = 40, m∠B = ____

23. Wrap-up
Today you learned to prove triangles congruent using the ASA and AAS Postulates
Tomorrow you’ll learn about the HL Theorem and about and how to use CPCTC.
Homework:
pp. 197 – 199: 1 – 29,
31-34: write the proof if you can deduce the conclusion from the given
Quiz on Wednesday on 4-1, 4-2, and 4-3