CHAPTER 4: CONGRUENT TRIANGLES Section 4-2

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Some Ways to Prove Triangles Congruent

TRIANGLE CONGRUENCE

When two triangles are congruent, the six parts of one triangle are congruent to the six corresponding parts of the other triangle.

There are ways to prove triangles congruent by comparing only three pairs of corresponding parts, which is the focus of this section.

POSTULATE 12: SSS POSTULATE

Postulate 12 (SSS Postulate):

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

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POSTULATE 13: SAS POSTULATE

Postulate 13 (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.

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POSTULATE 14: ASA POSTULATE

Postulate 14 (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.

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PRACTICE 1.

Decide whether you can deduce by SSS, SAS, or ASA Postulate that the two triangles are congruent.

1. Triangles are congruent by SSS.

2.

3.

2. Triangles are not congruent.

3. Triangles are congruent by SAS.

CLASSWORK/HOMEWORK

• Classwork: Pg. 123-124 Classroom Exercises 1-10 • Homework: Pg. 124-125 Written Exercises 1-16