Question

Two congruent triangles have the following corresponding parts: ∆RS ≅ ∆UV, ∆RT ≅ ∆UW, and ∠R ≅ ∠U. Which is NOT necessarily a correct congruence statement?

a) ∆RS ≅ ∆UV
b) ∆RT ≅ ∆UW
c) ∠R ≅ ∠U
d) ∆RS ≅ ∆RT

Answer 1

The correct congruence statement that is NOT necessarily correct is ∆RS ≅ ∆RT.

Step-by-step explanation:

The correct congruence statement would be d) ∆RS ≅ ∆RT.

In the given problem, it is stated that ∠R ≅ ∠U, meaning that corresponding angles are congruent in the two triangles. When two triangles are congruent, their corresponding sides and corresponding angles are equal. Therefore, ∆RS ≅ ∆UV (a), ∆RT ≅ ∆UW (b), and ∠R ≅ ∠U (c) are all true congruence statements. However, ∆RS ≅ ∆RT is not necessarily correct because no information is given about the relationship between side RS and side RT.