Triangle Congruence: SSS and HL — Quiz

Question 11 • Geometry

Which shows two triangles that are congruent by the SSS congruence theorem?

Answer

Image with description Triangles A B C and D E C are connected at point C. Angles A B C and C E D are right angles. The side lengths are A B and E D are congruent.

Image with description Triangles A B C and D E C are connected at point C. The lengths of sides A B and D E are congruent. The lengths of sides B C and C D are congruent.

Image with description Triangles A B C and D E C are connected at point C. The lengths of sides A C and C E are congruent. Angles B A C and C E D are congruent.

Image with description Triangles A B C and A D C share a common side A C. The side lengths of A B and A D are congruent. The side lengths of B C and D C are congruent.

Explanation

SSS requires all three pairs of corresponding sides to be congruent. In choice D, AB = AD and BC = DC are given, and the triangles share side AC, so AC = AC. Thus all three side pairs match, and the triangles are congruent by SSS.

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