Question

are the polygons below similar? 6 12 16 8 yes no

Explanation:

Step1: Recall similarity of rectangles

For two rectangles to be similar, the ratios of their corresponding sides must be equal. Let's denote the first rectangle (EFGH) with length \( l_1 = 12 \) and width \( w_1 = 6 \), and the second rectangle (VWUT) with length \( l_2 = 16 \) and width \( w_2 = 8 \) (assuming the sides are length and width, we need to check the ratio of length to width for both).

Step2: Calculate the ratio for the first rectangle

Ratio \( r_1=\frac{\text{length}}{\text{width}}=\frac{12}{6} = 2 \)

Step3: Calculate the ratio for the second rectangle

Ratio \( r_2=\frac{\text{length}}{\text{width}}=\frac{16}{8}=2 \)

Since the ratios of corresponding sides are equal (both equal to 2) and all angles in rectangles are right angles (so corresponding angles are equal), the two rectangles are similar.

Answer:

yes