Question

Which of the following statements is true about polygons with proportional corresponding sides?

A) Yes, it is always possible for polygons to have proportional corresponding sides and not be similar.

B) No, polygons with proportional corresponding sides are always similar.

C) It depends on the number of sides in the polygons.

D) Proportional corresponding sides are not a relevant factor in determining polygon similarity.

Answer 1

The statement that polygons with proportional corresponding sides are always similar is true, since this implies that both angles and sides maintain consistent proportions, which is necessary and sufficient for polygon similarity.

Step-by-step explanation:

The question addresses the concept of similarity in polygons, particularly focusing on whether proportional corresponding sides are sufficient for polygons to be similar. The statement that polygons with proportional corresponding sides are always similar is true.

For polygons to be similar, all their corresponding angles must be equal, and their corresponding sides must be proportional. This proportionality is a necessary condition for similarity, but it is also sufficient because it implies the angles are consistent which maintains the shape's proportions. Therefore, answer B is the correct assertion: No, polygons with proportional corresponding sides are always similar.