Question

right triangle abc is reflected over \\(\overline{ac}\\), then dilated by a scale factor of \\(\frac{2}{3}\\) to form triangle dec. which statements about the two triangles must be true? select three options. \\(\square \triangle abc \sim \triangle dec\\) \\(\square \angle b \cong \angle e\\) \\(\square 3bc = 2ec\\) \\(\square 3de = 2ab\\) \\(\square 3m\angle a = 2m\angle d\\) \\(\square 2m\angle a = 3m\angle d\\)

Explanation:

Step1: Analyze transformations

Reflection preserves shape/size; dilation preserves shape (similarity). So △ABC ~ △DEC.

Step2: Check angle congruence

Similar triangles have congruent angles. ∠B ≅ ∠E.

Step3: Relate side lengths

Scale factor k = 2/3: DEC sides = (2/3)ABC sides. So DE = (2/3)AB → 3DE=2AB.

Step4: Evaluate other options

3BC=2EC would mean EC=(3/2)BC, but EC=(2/3)BC (since BC corresponds to EC). Angles are congruent, so 3m∠A=2m∠D and 2m∠A=3m∠D are false.

Answer:

△ABC ~ △DEC, ∠B ≅ ∠E, 3DE = 2AB