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**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

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HW #32 Answer pg 243 # 1-19 all

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**Conditions for HL Theorem:**

There are two right triangles The triangles have congruent hypotenuse There is one pair of congruent legs

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**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.

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**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.

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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.

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**Proof Practice: Don’t peek at answer, try it!!**

4. Given: FAB GED, ABC EDC, AC EC Prove: ABC EDC

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**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

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

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