Question

is rstu similar to abcd? justify your answer.
yes, because a rotation 180° around the origin maps rstu onto abcd.
yes, because a translation left 8 units and down 7 units maps rstu onto abcd.
no, because ∠r and ∠a do not have the same measure.

Explanation:

Step1: Analyze the properties of similar figures

Similar figures have corresponding angles equal and corresponding sides in proportion.

Step2: Check the first two options

A rotation of \(180^{\circ}\) around the origin or a translation left \(8\) units and down \(7\) units are rigid transformations. Rigid transformations preserve congruence (not just similarity). But from the figure, the shapes do not look congruent (by visual inspection of side - lengths and angles).

Step3: Check the third option

For two figures to be similar, all corresponding angles must be equal. If \(\angle R\) and \(\angle A\) do not have the same measure, then the figures are not similar.

Answer:

No, because \(\angle R\) and \(\angle A\) do not have the same measure.