Question

determine if polygon j k l m is similar to polygon p q r s. if the polygons are similar, identify the similarity ratio. *note: figures not drawn to scale. a. yes, the polygons are similar. the similarity ratio is \frac{3}{5}. b. yes, the polygons are similar. the similarity ratio is \frac{1}{2}. c. no, the polygons are not similar. the corresponding angles are not congruent. d. no, the polygons are not similar. the corresponding sides are not proportional.

Explanation:

Step1: Check if the polygons are parallelograms

Both polygons \(JKLM\) and \(PQRS\) are parallelograms (opposite sides are equal). In a parallelogram, opposite angles are congruent and consecutive angles are supplementary. So, the corresponding angles of two parallelograms are congruent.

Step2: Check the ratio of corresponding sides

For parallelogram \(JKLM\) and \(PQRS\), let's find the ratio of the shorter sides and the longer sides.
The ratio of the shorter sides: \(\frac{9}{18}=\frac{1}{2}\)
The ratio of the longer sides: \(\frac{15}{30}=\frac{1}{2}\)

Since the ratios of the corresponding sides are equal (\(\frac{1}{2}\)) and corresponding angles are congruent (property of parallelograms), the polygons are similar.

Answer:

B. Yes, the polygons are similar. The similarity ratio is \(\frac{1}{2}\)