Question

Triangle A B C is reflected over side A C and then is dilated to form smaller triangle D E C. Angles B C A and D C E are right angles.
Right triangle ABC is reflected over AC, then dilated by a scale factor of Two-thirds to form triangle DEC. Which statements about the two triangles must be true? Select three options.

△ABC ~ △DEC
∠B ≅ ∠E
3BC = 2EC
3DE = 2AB
3m∠A = 2m∠D
2m∠A = 3m∠D

Answer 1

Correct choices:
- △ABC ~ △DEC
- ∠B ≅ ∠E
- 3DE = 2AB

Reasoning (brief):
- A reflection and a dilation preserve angle measures, so △ABC is similar to △DEC. The correspondence is A → D, B → E, C → C (C is fixed), so ∠B corresponds to ∠E.
- The dilation scale factor is 2/3, so each side of DEC is (2/3) of the corresponding side of ABC. In particular DE = (2/3)AB, hence 3DE = 2AB.
- The other algebraic/angle equations are not consistent with m∠A = m∠D or the 2/3 scale factor, so they are false.