1. 4-5 Triangle Congruence: ASA, AAS & HL
Geometry

2. 4-5 Triangle Congruence: ASA, AAS & HL Post 4-5-1 Angle-Side-Angle (ASA)  post
If 2 s and the included side of one Δ are  to the corresponding s and included side of another Δ, then the 2 Δs are .

3. B (( C )
If A  Z, C  X and , then Δ ABC  Δ ZYX. A Y ( Z )) X

4. Thm 4-5-2 Angle-Angle-Side (AAS)  thm
If 2 s and a non-included side of one Δ are  to the corresponding s and non-included side of another Δ, then the 2 Δs are .

5. If A  R, C  S, and , then ΔABC  ΔRQS.) A
If A  R, C  S, and , then ΔABC  ΔRQS. (( C S )) Q ) R

6. Thm 4-5-3 Hypotenuse-Leg (HL) Congruence
If the hypotenuse and a leg of a rt are
to the hypotenuse and a leg of another rt then the ‘ s are .

7. Ex. 1) Is it possible to prove the Δs are ?( ) )) )) (( ) ( ((
_______________
____________

8. Example 2 Given that B  C, D  F, M is the midpoint of seg DF
Prove Δ BDM  Δ CFM B C ) ) (( )) D M F

9. Proof for Ex. 2 Statements Reasons ________________
___________________
2. _________________
3. ________________
Reasons
1. ________________
2._________________
3. ________________

10. Example 3 X ) (( W Z (( ) Y Given that bisects XZY and XWY
Prove that Δ Δ WZY X ) (( W Z (( ) Y

11. Proof for Ex. 3 Statements 1.________________ __________________
2. _______________
3. _________________
4. _________________
Reasons
1. _________________
2. _________________
3. ________________
4. _________________

12. Example 4) Determine if you can use the HL Congruence Theorem to prove the triangles are congruent.
ABE and DCE, given that E is the midpoint of A B E C D no

13. THERE IS NO AAA (CAR INSURANCE) OR BAD WORDS

14. Assignment

15. 4.5 Using  Δs
Geometry

16. Once you know that Δs are , you can state that their corresponding parts are . CPCTC-corresponding parts triangles

17. CPCTC
Ex 1: P N L ) ( M

18. Proof 1: Statements 1. 2. ΔPMN  ΔPML Reasons Given Reflex. Prop
Def’n angle bisector
SAS
CPCTC

19. Assignment

20. Proof 1. Given A  R,C  S, 2. 3rd angles thm 3. ASA post
2. B  Q
3. Δ ABC  Δ RQS