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 the same shape but not necessarily the same size. Their corresponding angles are equal, and their corresponding sides are in proportion.

Step2: Check the given options

• A rotation or translation alone (without a dilation) cannot change the size of a figure. If \(RSTU\) and \(ABCD\) were similar, there should be a dilation factor. But the options of rotation (\(180^{\circ}\)) and translation (left 8 units and down 7 units) do not involve a dilation.
• For the third option, if \(\angle R\) and \(\angle A\) do not have the same measure, then the figures are not similar (since one of the key properties of similar figures - equal corresponding angles - is violated).

Answer:

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