Upload
mary-bloodsworth
View
225
Download
5
Tags:
Embed Size (px)
Citation preview
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