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4-5 Triangle Congruence: ASA, AAS, and HL Holt Geometry Warm Up Warm Up Lesson Presentation Lesson Presentation Lesson Quiz Lesson Quiz

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Warm Up 1. What are sides AC and BC called? Side AB? 2. Which side is in between A and C? 3. Given DEF and GHI, if D G and E H, why is F I? legs; hypotenuse AC Third s Thm. 4.5 Congruent Triangles by HL

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Apply HL to construct triangles and to solve problems. Prove triangles congruent by using HL. Objectives 4.5 Congruent Triangles by HL

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included side Vocabulary 4.5 Congruent Triangles by HL

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Example 1: 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. 4.5 Congruent Triangles by HL

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Example 2: 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. 4.5 Congruent Triangles by HL

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Check It Out! Example 3 Determine if you can use the HL Congruence Theorem to prove ABC DCB. If there is, provide a paragraph and two column proof. 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. 4.5 Congruent Triangles by HL

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Check It Out! Example 3 Continue 4.5 Congruent Triangles by HL 4. ABC DCB 4. By HL 3. Reflexive Prop. Leg 3. CB BC 2. Given Hypotenuse 2. AC DB. 1. Given Right Angle 1. ABC DCB ReasonsStatements

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Lesson Quiz: Part I Identify the postulate or theorem that proves the triangles congruent and create a two column proof. HL 4.5 Congruent Triangles by HL A B C D

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Lesson Quiz: Part I Continued 4. ADC ADB 4. By HL 3. Given Leg 3. CD BD 2. Given Hypotenuse 2. AB AC. 1. Given Right Angle 1. ADB ADC ReasonsStatements 4.5 Congruent Triangles by HL A BC D

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Lesson Quiz: Part II Identify the postulate or theorem that proves the triangles congruent and create a two column proof. HL 4.5 Congruent Triangles by HL A B C D

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Lesson Quiz: Part Ii Continued 4. ADC ADB 4. By HL 3. Given Leg 3. CD BD 2. Given Hypotenuse 2. AB AC. 1. Given Right Angle 1. ADB ADC ReasonsStatements 4.5 Congruent Triangles by HL A BC D

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