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

4.5 Congruent Triangles by HL 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.

Objectives 4.5 Congruent Triangles by HL 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

Example 1: Applying HL Congruence 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.

Example 2: Applying HL Congruence 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 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 Reasons Statements

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 B C D

4.5 Congruent Triangles by HL A Lesson Quiz: Part I Continued C B D 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 Reasons Statements

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 B C D

4.5 Congruent Triangles by HL A Lesson Quiz: Part Ii Continued C B D 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 Reasons Statements