4-5

1. 4-5 Triangle Congruence: HL Holt Geometry Warm Up Lesson Presentation Lesson Quiz

2. Warm Up • 1.What are sides AC and BC called? Side AB? legs; hypotenuse

3. Objective SWBAT prove triangles congruent by using HL.

5. Example 4A: Applying HL Congruence Determine if you can use the HL Congruence Theorem to prove the triangles congruent. If not, tell what else you need to know. According to the diagram, the triangles are right triangles that share one leg. It is given that the hypotenuses are congruent, therefore the triangles are congruent by HL.

6. Example 4B: Applying HL Congruence This conclusion cannot be proved by HL. According to the diagram, the triangles are right triangles and one pair of legs is congruent. You do not know that one hypotenuse is congruent to the other.

7. 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. Check It Out! Example 4 Determine if you can use the HL Congruence Theorem to prove ABC  DCB. If not, tell what else you need to know.

8. Lesson Quiz: Part I Identify the postulate or theorem that proves the triangles congruent. HL ASA SAS or SSS

9. Lesson Quiz: Part II 4. Given: FAB  GED, ABC   DCE, AC  EC Prove: ABC  EDC

10. Statements Reasons 1. FAB  GED 1. Given 2. BAC is a supp. of FAB; DEC is a supp. of GED. 2. Def. of supp. s 3. BAC  DEC 3.  Supp. Thm. 4. ACB  DCE; AC  EC 4. Given 5. ABC  EDC 5. ASA Steps 3,4 Lesson Quiz: Part II Continued