Question

1. in congruent triangles, if the side - lengths of triangle a are given as 5, 7, 8 and for triangle b are 8, 5, 7, what can be concluded about the two triangles using sss? triangles are not congruent triangle b is larger than triangle a triangle a is larger than triangle b triangles are congruent

Explanation:

The SSS (Side - Side - Side) congruence criterion states that if the three sides of one triangle are equal in length to the three corresponding sides of another triangle, then the two triangles are congruent. For triangle A, the side lengths are 5, 7, 8. For triangle B, the side lengths are 8, 5, 7. We can re - order the side lengths of triangle B to 5, 7, 8 (since the order of sides does not matter for congruence, only the set of side lengths). Now we can see that the three side lengths of triangle A (5, 7, 8) are exactly equal to the three side lengths of triangle B (when re - ordered). So by the SSS congruence criterion, the two triangles are congruent. The options that say the triangles are not congruent or that one is larger than the other are incorrect because congruent triangles have the same size and shape, meaning their corresponding sides are equal.

Answer:

D. Triangles are Congruent