Question

Explain the Error: Ava wants to know the distance JK across a pond. She locates points as shown. She says that the distance across the pond must be 160ft by the SSS Triangle Congruence Theorem. Explain her error.

Answer 1

Answer: Ava incorrectly applied the SSS triangle Congruence Theorem. The SSS triangle Congruence Theorem states that if the three sides of one triangle are congruent to the three sides of another triangle, then the two triangles are congruent. In this case Ava is assuming that the two triangles formed by the line across the pond are congruent, and therefore, the distance JK must be 160 ft. However, the fact that the two triangles share a side does not necessarily mean they are congruent. Therefore, Avas conclusion that the distance is 160 ft is not necessarily true.