CHAPTER 8PROVING

TRIANGLES CONGRUENT

Lesson #1

Congruent TrianglesEssential Question #1

If an isosceles triangle is folded along the bisector of the vertex angle, are the two triangles formed congruent, why or why

not?

Congruent TrianglesAre the following triangles congruent? Why or

why not?

Write a congruence statement for the triangles.

21°74°85°

21°74°85° T

S

R

L

M

N

Example 1Write a congruence statement for the set of

triangles.

Example 2Given , AB = 15, BC = 20, AC = 25, and FE

= 3x – 7, find x.

HOMEWORKPractice Worksheet 4-3

Congruent Triangles

DO YOU NEED TO HAVE ALL SIX CONGRUENT PARTS IN ORDER TO

DETERMINE IF TWO TRIANGLES ARE CONGRUENT?NO!!

!

4 Ways to Prove Triangles are Congruent

1. Side-Side-Side Postulate (SSS)2. Side-Angle-Side Postulate (SAS)3. Angle-Side-Angle Postulate

(ASA)4. Angle-Angle-Side Theorem

(AAS)

Side-Side-Side Postulate(SSS)

If the sides of one triangle are congruent to the sides of a second

triangle, then the triangles are congruent.

Side-Angle-Side Postulate(SAS)

If two sides and the included angle of one

triangle are congruent to two sides and the

included angle of another triangle, then the

triangles are congruent.

Angle-Side-Angle Postulate(ASA)

If two angles and the included side of one

triangle are congruent to two angles and the

included side of another triangle, then the

triangles are congruent.

Angle-Angle-Side Theorem(AAS)

If two angles and a non-included side of one triangle are congruent to two angles and a

non-included side of another triangle, then the triangles are congruent.

Example 3Determine whether the triangles are congruent. If they

are indicate the congruence postulate.

Example 4Determine whether the triangles are congruent. If they

are indicate the congruence postulate.

Example 5Determine whether Explain.

A(-3,3), B(-1,3), C(-3,1)K(1,4), L(3,4), M(1,6)

HOMEWORKPage 410 #6-14

Page 416 #1-12, not 4, 6, 9

Hypotenuse-Leg PostulateHL

If the hypotenuse and a leg of one triangle are congruent to the hypotenuse and a leg

of another right triangle, then the

triangles are congruent.

Example 6Determine whether the triangles are congruent. If they

are indicate the congruence postulate.

HOMEWORKPage 422 #2-6