Question

The two scalene triangles shown are similar but not congruent. ∠BCA ≅ ∠CAD. Which statement is true?

answer choices

a-∠BAC corresponds to ∠CDA. c-Side BC corresponds to side CD.

b-∠ADC corresponds to ∠ACB. d-Side AD corresponds to side BC.

Answer 1

a) ∠BAC corresponds to ∠CDA

Explanation:

We assume that the statement ∠BCA ≅ ∠CAD is supposed to mean ΔBCA ~ ΔCAD.

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For any statement about correspondence to be true, the order of the vertex names in the statement must match the order of the vertex names in the similarity claim.

Here, the letters of ∠BAC are the 1st, 3rd, and 2nd letters of the name of the first triangle in the assumed similarity statement. The 1st, 3rd, and 2nd letters in the name of ΔCAD are C, D, A, so corresponding angles are ...

∠BAC and ∠CDA . . . . . matches answer choice A

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Comment on the problem statement

As written here, ∠C in the first triangle corresponds to ∠A in the second triangle. This tells you nothing about the relationships of the other angles or sides. That is why we have to assume a similarity statement is intended. Otherwise, the problem cannot be appropriately answered.