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4.3 Analyzing Triangle Congruence. Objectives. Identify and use the SSS, SAS, and ASA Congruence Postulates and the AAS and HL Congruence Theorems. Use counterexamples to prove that other side and angle combinations cannot be used to prove triangle congruence. 4.3 Analyzing Triangle Congruence.

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Objectives

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Objectives

4.3 Analyzing Triangle Congruence

Objectives

  • Identify and use the SSS, SAS, and ASA Congruence Postulates and the AAS and HL Congruence Theorems.

  • Use counterexamples to prove that other side and angle combinations cannot be used to prove triangle congruence.


Theorems postulates definitions

4.3 Analyzing Triangle Congruence

Theorems, Postulates, & Definitions

AAS (Angle-Angle-Side) Congruence Theorem 4.3.1: If two angles and a nonincluded

side of one triangle are congruent to the corresponding angles and nonincluded side of another triangle, then the triangles are congruent.

HL (Hypotenuse-Leg) Congruence Theorem

4.3.2: If the hypotenuse and a leg of a right

triangle are congruent to the hypotenuse and

a leg of another right triangle, then the two triangles are congruent.


Key skills

TOC

4.3 Analyzing Triangle Congruence

Key Skills

Use AAS and HL Theorems to determine

whether triangles are congruent.

a. ABCDCB

by HL Theorem.

b. WXYWZY

by AAS.

c. PRS may not be congruent to ONM

because triangles cannot be proven congruent by SSA.


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