Congruence Criteria Math Example 1

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Example 1

easy
Two triangles share the following information: AB=DE=5AB = DE = 5, BC=EF=7BC = EF = 7, AC=DF=9AC = DF = 9. Are the triangles congruent? State the congruence criterion used.

Solution

  1. 1
    Step 1: List what is known: all three pairs of corresponding sides are equal — AB=DEAB = DE, BC=EFBC = EF, AC=DFAC = DF.
  2. 2
    Step 2: Identify the applicable congruence criterion. When all three sides of one triangle equal the corresponding sides of another, we use SSS (Side-Side-Side).
  3. 3
    Step 3: Conclude: By SSS, △ABC≅△DEF\triangle ABC \cong \triangle DEF.

Answer

△ABC≅△DEF\triangle ABC \cong \triangle DEF by SSS.
SSS (Side-Side-Side) congruence states that if all three sides of one triangle are equal in length to the corresponding sides of another triangle, the triangles are congruent. This works because the shape of a triangle is completely determined by its three side lengths.

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).

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More Congruence Criteria Examples

Example 2 medium

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Example 3 easy

Match each situation to the correct congruence criterion (SSS, SAS, ASA, AAS, HL): Two triangles hav

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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