Name all the things that can you conclude from each diagram?. 1. 2 things2. 3 things3.4 things Warm Up.

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Presentation transcript:

Name all the things that can you conclude from each diagram? things2. 3 things3.4 things Warm Up

4.2: Proving Triangles are Congruent by SSS and SAS Objectives:  Prove that triangles are congruent using SSS and SAS Congruence Postulates.  Use congruence postulates in real-life problems.

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

Ways to Prove 2 Triangles Congruent 1. All sides and All angles are congruent 2. SSS 3. SAS

Postulate 4-1: Side-Side-Side (SSS) Congruence Postulate If three sides of one triangle are congruent to three sides of a second triangle, then the two triangles are congruent.

Checkpoint? Is there enough information given to prove that the two triangles are congruent? Explain. Is there enough information given to prove that the two triangles are congruent? Explain. L M P N

Write a paragraph proof. Given: M is the midpoint of XY, AX AY Prove: AMX AMY Triangle 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) Congruence Postulate If two sides and the included angle of one triangle are congruent to two sides and the included angle of second triangle, then the two triangles are 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 Section 4.2 Pages #1-11, 14-21, 23-27