Congruence Criteria Math Example 3

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Example 3

easy
Match each situation to the correct congruence criterion (SSS, SAS, ASA, AAS, HL): Two triangles have two angles and the included side equal.

Solution

  1. 1
    Step 1: 'Two angles and the included side' means: ∠A=∠D\angle A = \angle D, AB=DEAB = DE, ∠B=∠E\angle B = \angle E — the side is between the two known angles.
  2. 2
    Step 2: This matches ASA (Angle-Side-Angle): two angles and the included side.

Answer

ASA (Angle-Side-Angle).
ASA states that two triangles are congruent if two angles and the included side (the side between those two angles) of one triangle equal the corresponding parts of the other. The included side is what distinguishes ASA from AAS, where the side is not between the two angles.

About Congruence Criteria

Five sets of conditions that guarantee two triangles are congruent: SSS (three pairs of equal sides), SAS (two sides and the included angle), ASA (two angles and the included side), AAS (two angles and a non-included side), and HL (hypotenuse-leg for right triangles).

Learn more about Congruence Criteria →

More Congruence Criteria Examples

Example 1 easy

Two triangles share the following information: [formula], [formula], [formula]. Are the triangles co

Example 2 medium

In right triangles [formula] and [formula], both have a right angle. The hypotenuse [formula] and le

Example 4 hard

Explain why SSA (two sides and a non-included angle) is NOT a valid congruence criterion by giving a

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