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**Entry task Socractive Multiple Choice**

A – Yes, continue to make the assignments online as much as possible B – No, I don’t want any more online assignments C – A even mix is good

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**4.6 Congruence in Right Triangles**

Learning Target I can prove triangles congruent by using Hypotenuse – Leg Theorem. (HL) Success Criteria: I understand HL and can use it correctly in a proof

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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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**At your tables Proof Statements | Reasons PS = QR 1)Given**

PR = PR ) reflexive <QPR and <PRS are rt 3) Given PRS = PRQ 4) HL

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Assignment Homework – p. 261 #1-13 odds, 16-18, Challenge - # 28

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Exit Slip Identify the postulate or theorem that proves the triangles congruent. HL ASA SAS or SSS

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**Do Now: Discuss a Plan with your group!**

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

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**Lesson Quiz: Part II Continued**

5. ASA 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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Objectives Apply ASA, AAS, and HL to construct triangles and to solve problems. Prove triangles congruent by using ASA, AAS, and HL.

Objectives Apply ASA, AAS, and HL to construct triangles and to solve problems. Prove triangles congruent by using ASA, AAS, and HL.

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