Question

are the shapes similar? complete the explanation.
the shapes (select) similar. all of the angles are (select) angles and the ratio of the corresponding sides is 3:
there are two squares (or rectangles with all sides equal) shown: one with side length 15 ft (all angles 90°) and one with side length 25 ft (all angles 90°).

Explanation:

Step1: Check Angle Condition

Both shapes are rectangles (all angles \(90^\circ\)), so corresponding angles are equal (congruent).

Step2: Check Side Ratio

First shape side: \(15\) ft, second: \(25\) ft. Ratio of sides: \(\frac{15}{25}=\frac{3}{5}\), so ratio is \(3:5\).

Step3: Similarity Check

For similarity, angles congruent and sides proportional. Both hold, so shapes are similar.

Answer:

The shapes \(\boldsymbol{\text{are}}\) similar. All of the angles are \(\boldsymbol{\text{congruent}}\) angles and the ratio of the corresponding sides is \(3:\boldsymbol{5}\).