Happy Tuesday 

1. Happy Tuesday  Do Before the Bell Rings: • Pick up the paper from the front table • Take out notes from yesterday • Have your homework out on your desk with a red pen. • Take out your whiteboard and whiteboard pens. Math History Presentations will be TODAY!

2. Math History Presentations

3. Warm Up: Whiteboards • 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? legs; hypotenuse Third s Thm.

4. Example from yesterday: Verifying Triangle Congruence Show that the triangles are congruent for the given value of the variable. ∆MNO  ∆PQR, when x = 5. PQ  MN, QR  NO, PR  MO ∆MNO  ∆PQR by SSS.

5. ST  VW, TU  WX, and T  W. Whiteboards Show that the triangles are congruent for the given value of the variable. ∆STU  ∆VWX, when y = 4. ∆STU  ∆VWX by SAS.

6. 4-4 Triangle Congruence: SSS and SAS Example 3 ( from yesterday): The Hatfield and McCoy families are feuding over some land. Neither family will be satisfied unless the two triangular fields are exactly the same size. You know that BC is parallel to AD and the midpoint of each of the intersecting segments. Write a two-column proof that will settle the dispute. . Prove: ∆ABD ∆CDB Proof: Given: BC|| AD, BC AD

7. 4.5: Triangle Congruence: ASA, AAS, and HL Learning Objective • SWBAT prove triangles congruent by using ASA, AAS, and HL.

8. Math Joke of the Day • What do you call a broken angle? • A rectangle!

9. 4.5Triangle Congruence: SSS and SAS There are five ways to prove triangles are congruent: • SSS yesterday • SAS • ASA Today! • AAS • HL

10. Included Side • Yesterday we learned what an included angle is. What do you think an included side would be?

11. Included side • common side of two consecutive angles in a polygon.

12. 4-4 Triangle Congruence: SSS and SAS Angle–Side–Angle Congruence (ASA) • If two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the triangles are congruent • . What is a possible congruent statement for the figures?

13. ASA • Examples • Non-Examples

14. Example 1 Example 1: • Use ASA to explain why ∆UXV ∆WXV.

15. By the Alternate Interior Angles Theorem. KLN  MNL. NL  LN by the Reflexive Property. No other congruence relationships can be determined, so ASA cannot be applied. Whiteboard Determine if you can use ASA to prove NKL LMN. Explain.

16. Angle-Angle-Side Congruence Angle-Angle-Side(AAS) • If two angles and a non-included side of one triangle are congruent to the corresponding angles and a side of a second triangle, then the two triangles are congruent. What is the possible congruence statement for the figures?

17. Example/ Non-Examples: AAS • Example • Non-Example

18. Proof of AAS Example 2:

19. Example 3 Use AAS to prove the triangles congruent. Given:JL bisects KLM, K  M Prove:JKL  JML

20. Hypotenuse-Leg (HL) Congruence Hypotenuse-Leg Congruence (HL) • If the hypotenuse and a leg of a right triangle are congruent to the hypotenuse and a leg of another right triangle, then the triangles are congruent.

21. Examples/Non-Examples: HL • Example • Non-Example

22. Yes; it is given that AC DB. BC  CB by the Reflexive Property of Congruence. Since ABC and DCB are right angles, ABC and DCB are right triangles. ABC  DCB by HL. Example 4 Prove ABC  DCB.

23. Whiteboards Identify the postulate or theorem that proves the triangles congruent. HL ASA SAS or SSS

24. Homework • Worksheet online! • The answers are on the bottom but try it yourself first • I will not be here tomorrow