4.6 Congruence in Right Triangles I can prove triangles congruent by using Hypotenuse – Leg Theorem. Do Now: Identify the postulate or theorem that proves the triangles congruent. SSS ASA SAS or SSS Success Criteria: Today’s Agenda Prove triangles congruent by hypotenuse leg Prove parts congruent and measure distance Do Now Check HW Lesson Assignment

HW #32 Answer pg 243 # 1-19 all

Conditions for HL Theorem: There are two right triangles The triangles have congruent hypotenuse There is one pair of congruent legs

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.

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.

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. 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.

Proof Practice: Don’t peek at answer, try it!! 4. Given: FAB  GED, ABC   EDC, AC  EC Prove: ABC  EDC

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

Assignment #33 pg 262-264 P: #10 - 13, 34 – 36 If you finish early please watch the video from your book and/or try the Geometry Quizzes on Dragonometry.net