Question

if the polygons are similar, identify the similarity ratio.
*note: figures not drawn to scale.
a. no, the polygons are not similar. the corresponding angles are not congruent.
b. no, the polygons are not similar. the corresponding sides are not proportional.
c. yes, the polygons are similar. the similarity ratio is $\frac{1}{2}$.
d. yes, the polygons are similar. the similarity ratio is $\frac{2}{3}$.

Explanation:

Step1: Check if corresponding angles are congruent

Both polygons are rectangles, and all angles in a rectangle are \(90^{\circ}\). So, corresponding angles are congruent.

Step2: Check if corresponding sides are proportional

For the first rectangle (EFGH), length \(l_1 = 10\) cm and width \(w_1=3\) cm. For the second rectangle (WXYZ), length \(l_2 = 15\) cm and width \(w_2 = 6\) cm.
Check the ratio of lengths: \(\frac{l_1}{l_2}=\frac{10}{15}=\frac{2}{3}\)
Check the ratio of widths: \(\frac{w_1}{w_2}=\frac{3}{6}=\frac{1}{2}\)
Since \(\frac{2}{3}
eq\frac{1}{2}\), the corresponding sides are not proportional.

Answer:

B. No, the polygons are not similar. The corresponding sides are not proportional.