Question

determine if the figures are similar. if they are give the similarity ratio. rectangles abcd and wxyz

Explanation:

Step1: Identify side ratios

For rectangle \(ABCD\), sides are \(30\) and \(64\). For rectangle \(WXYZ\), sides are \(45\) and \(96\). Calculate ratios: \(\frac{30}{45}=\frac{2}{3}\), \(\frac{64}{96}=\frac{2}{3}\).

Step2: Check similarity

Since all angles in rectangles are \(90^\circ\) (equal) and side ratios are equal (\(\frac{2}{3}\)), the rectangles are similar.

Step3: Determine similarity ratio

The similarity ratio is the ratio of corresponding sides, e.g., \(\frac{30}{45}=\frac{2}{3}\) (or \(\frac{64}{96}=\frac{2}{3}\)).

Answer:

The rectangles are similar, and the similarity ratio is \(\frac{2}{3}\) (or \(2:3\)).