Question

which rectangles are similar?
a. abcd and pqrs
b. pqrs and defg
c. defg and vwxy
d. vwxy and abcd

Explanation:

Step1: Recall the condition for similar rectangles

For two rectangles to be similar, the ratios of their corresponding sides must be equal.

Step2: Calculate the ratios for each option

• Option A: \(ABCD\) and \(PQRS\)

The ratio of the longer sides: \(\frac{5.5}{5} = 1.1\), the ratio of the shorter sides: \(\frac{2.5}{3}\approx0.83\). Since \(1.1
eq0.83\), they are not similar.

• Option B: \(PQRS\) and \(DEFG\)

The ratio of the longer sides: \(\frac{5.5}{2}= 2.75\), the ratio of the shorter sides: \(\frac{2.5}{2.5}=1\). Since \(2.75
eq1\), they are not similar.

• Option C: \(DEFG\) and \(VWXY\)

The ratio of the longer sides: \(\frac{5}{2.5}=2\), the ratio of the shorter sides: \(\frac{4}{2}=2\). Since the ratios are equal, they are similar.

• Option D: \(VWXY\) and \(ABCD\)

The ratio of the longer sides: \(\frac{5}{5} = 1\), the ratio of the shorter sides: \(\frac{4}{3}\approx1.33\). Since \(1
eq1.33\), they are not similar.

Answer:

C. DEFG and VWXY