4-5 Triangle Congruence: ASA, AAS, and HL

Holt Geometry

Warm UpWarm Up

Lesson PresentationLesson Presentation

Lesson QuizLesson Quiz

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

Apply HL to construct triangles and to solve problems.

Prove triangles congruent by using HL.

Objectives

4.5 Congruent Triangles by HL

included side

Vocabulary

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

4.5 Congruent Triangles by HL

4. ABC DCB 4. By HL

3. Reflexive Prop. Leg3. CB BC

2. Given Hypotenuse2. AC DB.

1. Given Right Angle1. ABC DCB

ReasonsStatements

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

BCD

Lesson Quiz: Part I Continued

4. ADC ADB 4. By HL

3. Given Leg3. CD BD

2. Given Hypotenuse2. AB AC.

1. Given Right Angle1. ADB ADC

ReasonsStatements

4.5 Congruent Triangles by HLA

BC D

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

BCD

Lesson Quiz: Part Ii Continued

4. ADC ADB 4. By HL

3. Given Leg3. CD BD

2. Given Hypotenuse2. AB AC.

1. Given Right Angle1. ADB ADC

ReasonsStatements

4.5 Congruent Triangles by HLA

BC D