Bell-Ringer Given:, m<A = 2x+18, m<B = 3x+5, m< F = 7x+1 Find x

Section 4-2 Proving ∆’s Congruent

Goal: Prove two triangles are congruent. We are going to learn 5 ways!!!!

SSS Postulate If three sides of one triangle are congruent to three sides of another triangle, then the triangles are congruent.

SSS Side AB DE Side EF BC Side AC DF A B C D E F

SAS Postulate 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.

SAS Side TO PA Angle <O <A Side OM AT T OM P A T

ASA Postulate 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.

ASA Angle <L <J Included Side LR JN Angle <R <N J E N L A R

AAS Theorem If two angles and a non- included side of one triangle are congruent to the corresponding parts of another triangle, then the triangles are congruent.

AAS Angle <L <I Angle <J <G Non-Included Side JK GH G H I J K L

HL Theorem If the hypotenuse and a leg of one right triangle are congruent to the corresponding parts of another right triangle, then the triangle are congruent. Why is it true?

HL Right Triangle Hypotenuse LKIH Leg JK GH G H I J K L

There is a strategy that we want to use when proving that triangles or parts of triangles are congruent.

Proving two triangles are congruent Identify two triangles Use your colors to show what is congruent Make a statement for each congruent piece Say the triangles (in correct order!!) are congruent by…

Proving two segments or two angles congruent Identify the 2 triangles and their congruent pieces Prove the triangles to be congruent Use CPCTC to prove the parts congruent.

Let’s Practice!!!!

Homework Pg Written Exercises #1-15 Pg 142 Classroom Exercises #1-9