Question

d. are any two rectangles in which one side is twice as long as the other always similar? no yes

Explanation:

For two rectangles to be similar, the ratios of their corresponding sides must be equal. Let's assume one rectangle has sides \(a\) and \(2a\), and another rectangle has sides \(b\) and \(2b\). The ratio of the sides of the first rectangle is \(\frac{2a}{a}=2\), and the ratio of the sides of the second rectangle is \(\frac{2b}{b} = 2\). Also, all angles in rectangles are right angles (\(90^{\circ}\)). So, by the definition of similar polygons (equal - corresponding angles and proportional - corresponding sides), any two rectangles in which one side is twice as long as the other are similar.

Answer:

Yes