Name all the things that can you conclude from each diagram?.1. 2 things 2. 3 things 3. 4 things

Warm Up

4.2: 4.2: Proving Triangles are Congruent Proving Triangles are Congruent by SSS and SASby SSS and SAS

Objectives:Objectives: Prove that triangles are congruent using Prove that triangles are congruent using

SSS and SAS Congruence Postulates.SSS and SAS Congruence Postulates. Use congruence postulates in real-life Use congruence postulates in real-life

problems.problems.

How much information do How much information do you need to know to tell you need to know to tell whether two triangles are whether two triangles are

congruent?congruent?

Ways to Prove 2 Triangles CongruentWays to Prove 2 Triangles Congruent

1. All sides and All angles are congruent1. All sides and All angles are congruent

2. SSS2. SSS

3. SAS3. SAS

Postulate 4-1: Side-Side-Side (SSS) Postulate 4-1: Side-Side-Side (SSS) Congruence PostulateCongruence Postulate

If three sides of one triangle are congruent to If three sides of one triangle are congruent to three sides of a second triangle, then the two three sides of a second triangle, then the two triangles are congruent.triangles are congruent.

Checkpoint?Checkpoint?

Is there enough information given to prove Is there enough information given to prove that the two triangles are congruent? that the two triangles are congruent? Explain.Explain.

L M

P N

Write a paragraph proof.

Given: M is the midpoint of XY, AX AY

Prove: AMX AMY

Triangle Congruence by SSSTriangle Congruence by SSS

Copy the diagram. Mark the congruent sides.

You are given that M is the midpoint of XY, and AX AY.

Midpoint M implies MX MY. AM AM by the Reflexive

Property of Congruence, so AMX AMY by the SSS

Postulate.

Postulate 4-2: Side-Angle-Side (SAS) Postulate 4-2: Side-Angle-Side (SAS) Congruence PostulateCongruence Postulate

If two sides and the If two sides and the includedincluded angle of one angle of one triangle are congruent triangle are congruent to two sides and the to two sides and the includedincluded angle of angle of second triangle, then second triangle, then the two triangles are the two triangles are congruent.congruent.

Given : C is the midpoint of AD and of BE

Prove: Triangle ABC = DEC

Copy the diagram. Mark what is given on the diagram.

Given: RSG RSH, SG SH From the information given, can you prove RSG RSH? Explain.

It is given that RSG RSH and SG SH. RS RS by the Reflexive Property of Congruence.

Two pairs of corresponding sides and their included angles are congruent, so RSG RSH by the SAS Postulate.

HW Assignment HW Assignment Section 4.2Section 4.2

Pages 189-191Pages 189-191

#1-11, 14-21, 23-27#1-11, 14-21, 23-27