4 5 Triangle Congruence ASA AAS and HL

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

4. 5 Congruent Triangles by HL Warm Up 1. What are sides AC and BC called? Side AB? legs; hypotenuse 2. Which side is in between A and C? AC 3. Given DEF and GHI, if D G and E H, why is F I? Third s Thm.

4. 5 Congruent Triangles by HL Objectives Apply HL to construct triangles and to solve problems. Prove triangles congruent by using HL.

4. 5 Congruent Triangles by HL Vocabulary included side

4. 5 Congruent Triangles by HL

4. 5 Congruent Triangles by HL 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 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 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 Check It Out! Example 3 Continue Statements Reasons 1. ABC DCB 1. Given Right Angle 2. AC DB. 2. Given Hypotenuse 3. CB BC 3. Reflexive Prop. Leg 4. ABC DCB 4. By HL

4. 5 Congruent Triangles by HL Lesson Quiz: Part I Identify the postulate or theorem that proves the triangles congruent and create a two column proof. A HL C D B

4. 5 Congruent Triangles by HL Lesson Quiz: Part I Continued C Statements A D Reasons 1. ADB ADC 1. Given Right Angle 2. AB AC. 2. Given Hypotenuse 3. CD BD 3. Given Leg 4. ADC ADB 4. By HL B

4. 5 Congruent Triangles by HL Lesson Quiz: Part II Identify the postulate or theorem that proves the triangles congruent and create a two column proof. A HL C D B

4. 5 Congruent Triangles by HL Lesson Quiz: Part Ii Continued C Statements A D Reasons 1. ADB ADC 1. Given Right Angle 2. AB AC. 2. Given Hypotenuse 3. CD BD 3. Given Leg 4. ADC ADB 4. By HL B