Which of the following statements is always true of similar polygons?
Corresponding angles of similar figures have the same measure.
• The lengths of corresponding sides form equivalent ratios.
• The lengths of corresponding sides have the same measure.
• both (a) and (b)
D
To determine which of the statements is always true of similar polygons, let's analyze each option:
Option (a): Corresponding angles of similar figures have the same measure.
This statement is true. In similar polygons, corresponding angles are equal. This means that if two polygons are similar, their corresponding angles will have the same measure.
Option (b): The lengths of corresponding sides form equivalent ratios.
This statement is also true. In similar polygons, the lengths of corresponding sides are proportional. This means that the ratio of the lengths of corresponding sides is constant.
Option (c): The lengths of corresponding sides have the same measure.
This statement is not always true. While the lengths of corresponding sides may be equal in some cases, the general rule is that they are proportional, not necessarily equal.
Therefore, the correct answer is option (a) and option (b) - both statements (a) and (b) are always true of similar polygons.
The correct answer is option (d) both (a) and (b).
In similar polygons, corresponding angles of the figures have the same measure. This means that if two angles in one polygon are equal, then their corresponding angles in the other polygon will also be equal.
Additionally, the lengths of corresponding sides in similar polygons form equivalent ratios. This means that if the ratio of the lengths of two corresponding sides in one polygon is a/b, then the ratio of the lengths of their corresponding sides in the other polygon will also be a/b.
Therefore, both (a) and (b) are always true of similar polygons.