Question

are the polygons below similar?
(image of two rectangles: left rectangle qprs with sides 20 and 10, right rectangle ghij with sides 30 and 15. options: yes, no)

Explanation:

Step1: Recall Similar Polygon Criteria

For polygons to be similar, corresponding angles must be equal, and corresponding sides must be in proportion. Both figures are rectangles (all angles are right angles, so angles are equal). Now check side ratios.

Step2: Identify Corresponding Sides

First rectangle (PQRS) has sides 20 and 10. Second rectangle (GHIJ) has sides 30 and 15.

Step3: Calculate Ratios

Ratio of length to length: $\frac{30}{20} = \frac{3}{2}$. Ratio of width to width: $\frac{15}{10} = \frac{3}{2}$. Ratios are equal, so sides are proportional.

Answer:

yes