Final answer:
Similar polygons must have congruent sides, proportional angles, and proportional sides.
Step-by-step explanation:
Similar polygons must have the following characteristics:
- A. Congruent Sides: The corresponding sides of similar polygons are proportional in length. For example, if one side of a polygon is twice as long as the corresponding side of another polygon, then all other corresponding sides will also have a ratio of 2:1.
- B. Proportional Angles: The corresponding angles of similar polygons are equal in measure. For example, if one angle in a polygon is 45 degrees, then the corresponding angle in a similar polygon will also be 45 degrees.
- C. Proportional Sides: This is essentially the same as congruent sides. The corresponding sides of similar polygons are proportional in length.
Final answer:
Similar polygons are defined by having proportional sides and congruent angles, which means the sides are of different lengths but hold a consistent ratio, and the angles have the exact same measure.
Step-by-step explanation:
Similar polygons must satisfy the conditions of having proportional sides and congruent angles.
Upon examining the characteristics that define similar polygons:
Therefore, options C and D are applicable. When two polygons are similar, they do not necessarily have congruent sides as their sides are proportional but can be of different lengths (ruling out option A). Also, they don't have proportional angles; instead, they have congruent angles, meaning the angles themselves are equal in measure (ruling out option B).