select the correct answer. which rectangles are similar? a. abcd and pqrs b. pqrs and defg c. defg and vwxy…

Explanation:

Step1: Recall similarity condition

Two rectangles are similar if the ratios of their corresponding sides are equal.

Step2: Calculate ratio for ABCD and PQRS

For rectangle (ABCD) with sides (3) cm and (5) cm, and rectangle (PQRS) with sides (2.5) cm and (5.5) cm. The ratio of the shorter - sides is (\frac{3}{2.5}=\frac{30}{25}=\frac{6}{5}), and the ratio of the longer - sides is (\frac{5}{5.5}=\frac{50}{55}=\frac{10}{11}). Since (\frac{6}{5}\neq\frac{10}{11}), they are not similar.

Step3: Calculate ratio for PQRS and DEFG

For rectangle (PQRS) with sides (2.5) cm and (5.5) cm, and rectangle (DEFG) with sides (2) cm and (2.5) cm. The ratio of the shorter - sides is (\frac{2.5}{2}=\frac{25}{20}=\frac{5}{4}), and the ratio of the longer - sides is (\frac{5.5}{2.5}=\frac{55}{25}=\frac{11}{5}). Since (\frac{5}{4}\neq\frac{11}{5}), they are not similar.

Step4: Calculate ratio for DEFG and VWXY

For rectangle (DEFG) with sides (2) cm and (2.5) cm, and rectangle (VWXY) with sides (4) cm and (5) cm. The ratio of the shorter - sides is (\frac{2}{4}=\frac{1}{2}), and the ratio of the longer - sides is (\frac{2.5}{5}=\frac{1}{2}). Since the ratios of the corresponding sides are equal, (DEFG) and (VWXY) are similar.

Step5: Calculate ratio for VWXY and ABCD

For rectangle (VWXY) with sides (4) cm and (5) cm, and rectangle (ABCD) with sides (3) cm and (5) cm. The ratio of the shorter - sides is (\frac{3}{4}), and the ratio of the longer - sides is (\frac{5}{5} = 1). Since (\frac{3}{4}\neq1), they are not similar.

Answer:

C. DEFG and VWXY