Tell whether the pair of polygons is similar or not. Explain why or why not 14 feet by 9 feet and 1 is 5.1 feet by 2.3 feet.

Answer 1

To determine if two polygons are similar, the corresponding angles must be equal, and the lengths of corresponding sides must be proportional. In this case, we are presumably talking about rectangles, which are a type of polygon.

Let's check the proportionality of the sides:

The sides of the first rectangle are 14 feet and 9 feet.
The sides of the second rectangle are 5.1 feet and 2.3 feet.

To check for proportionality, we need to find the ratios of the corresponding sides and see if they are constant (the same).

First pair of corresponding sides:
14 feet / 5.1 feet ≈ 2.7451

Second pair of corresponding sides:
9 feet / 2.3 feet ≈ 3.913

The two ratios are not the same, so the sides are not proportional. Hence, the two rectangles are NOT similar.

For rectangles (which have all right angles), the only requirement beyond angle congruence (which is already a given) is side proportionality. Since we've demonstrated that their corresponding sides are not in proportion, the rectangles cannot be considered similar.