To determine if two polygons are similar, we need to check two main properties:
1. Corresponding Angles:
- The corresponding angles of the two polygons must be congruent. This means that each angle in one polygon must be equal to the corresponding angle in the other polygon.
2. Corresponding Sides:
- The corresponding sides of the two polygons must be proportional. This indicates that the ratios of the lengths of corresponding sides are equal.
Given these properties, let's evaluate the choices provided:
- Choice A: Congruent... congruent
- Corresponding angles are congruent.
- Corresponding sides are congruent.
- This choice suggests both angles and sides are congruent, which defines congruent polygons, not similar polygons.
- Choice B: Congruent... proportional
- Corresponding angles are congruent.
- Corresponding sides are proportional.
- This defines similar polygons correctly!
- Choice C: Proportional... congruent
- Corresponding angles are proportional.
- Corresponding sides are congruent.
- This does not make sense in the context of similarity as angles cannot be proportional (they are either equal or not).
- Choice D: Proportional... proportional
- Corresponding angles are proportional.
- Corresponding sides are proportional.
- This choice is incorrect since angles being proportional is not a valid criterion; angles must be congruent (equal).
Based on the correct criteria for similarity of polygons, the best answer from the choices provided is:
B. Congruent... proportional
