Which of the following statements is always true of similar polygons? (1 point)
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)
correct
The correct statement that is always true of similar polygons is: both (a) and (b).
Explanation:
Similar polygons are polygons that have the same shape but not necessarily the same size. When polygons are similar, their corresponding angles have the same measure (statement a) and the lengths of their corresponding sides form equivalent ratios (statement b).
Therefore, both statement (a) and (b) are always true of similar polygons.
To determine which statement is always true of similar polygons, we need to understand what it means for polygons to be similar.
Similar polygons are figures that have the same shape, but not necessarily the same size. In other words, the corresponding angles of similar polygons are congruent (equal), and the corresponding sides are proportional (have equivalent ratios).
Now let's evaluate each statement:
Statement (a): "Corresponding angles of similar figures have the same measure."
This statement is true for similar polygons. When polygons are similar, their corresponding angles have the same measure. Therefore, statement (a) is always true.
Statement (b): "The lengths of corresponding sides form equivalent ratios."
This statement is also true for similar polygons. When polygons are similar, the ratios of the lengths of their corresponding sides are equivalent. For example, if you have two similar triangles, the ratio of any two corresponding sides will be the same. Therefore, statement (b) is always true.
Given that both statement (a) and statement (b) are true, the correct answer is "both (a) and (b)."