Question

On the grid below △ABC and △DEF are shown.

Which statement can be used to show △ABC ~ △DEF?
△DEF is the result of a translation followed by a reflection of △ABC, and all side lengths are preserved with these transformations.

△DEF is the result of a dilation followed by a rotation of△ABC, and all angle measures are preserved with these transformations.

△DEF is the result of a reflection followed by a dilation of △ABC, and all angle measures are preserved with these transformations.

△DEF is the result of a dilation followed by a rotation of△ABC, and all side lengths are preserved with these transformations.

Answer 1

△DEF is the result of a dilation followed by a rotation of △ABC, and all angle measures are preserved with these transformations

Explanation:

Not option 1: translation and reflection would not result in a smaller figure.

Not option 3: not a reflection.

Not option 4: side lengths aren't preserved - either in the figure nor with dilation in general.

Check:

1. Find all side lengths:
AB=2√2 DE=1√2
BC=5 EF=2.5
AC=√13≈3.6 DF=√3.25≈1.8

2. Since each pair of corresponding side lengths have equal ratios (2), the corresponding angle measures will be equal. (Verify with the Law of Sines if needed, after finding that m∠B=m∠E=45° by special right triangles.)