Entry task

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as much as possible• B – No, I don’t want any more online assignments• C – A even mix is good

Learning TargetI can prove triangles congruent by using

Hypotenuse – Leg Theorem. (HL)

Success Criteria: I understand HL and can use it correctly in a proof

4.6 Congruence in Right Triangles

Conditions for HL Theorem:There are two right trianglesThe triangles have congruent hypotenuseThere 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.

At your tables Proof

Statements | Reasons

1) PS = QR 1)Given

2) PR = PR 2) reflexive

3) <QPR and <PRS are rt 3) Given

4) PRS = PRQ 4) HL

Assignment

Homework – p. 261 #1-13 odds, 16-18, 23-25

Challenge - # 28

Exit Slip

Identify the postulate or theorem that proves the triangles congruent.

ASAHL

SAS or SSS

Do Now: Discuss a Plan with your group!

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

Prove: ABC EDC

Lesson Quiz: Part II Continued

5. ASA Steps 3,45. ABC EDC

4. Given4. ACB EDC; AC EC

3. Supp. Thm.3. BAC DEC

2. Def. of supp. s2. BAC is a supp. of FAB; DEC is a supp. of GED.

1. Given1. FAB GED

ReasonsStatements