What polygon is similar to every other polygon of the same name?
(A) triangle
(B) parallelogram
(C) rectangle
(D) square
(E) trapezoid
The correct answer is (D) square.
A square is a polygon that has four equal sides and four right angles. Any other square will have the same properties and therefore will be similar to every other square.
To determine which polygon is similar to every other polygon of the same name, we need to understand what it means for two polygons to be similar. Two polygons are said to be similar if their corresponding angles are congruent and their corresponding sides are in proportion.
Let's consider each option and determine if it satisfies the conditions for similarity:
(A) A triangle: While all triangles have three sides and three angles, not all triangles are similar. The corresponding angles of two triangles may be congruent, but their corresponding sides may not be in proportion. Therefore, option A is not the correct answer.
(B) A parallelogram: Parallelograms have four sides and four angles. It is possible for two parallelograms to have congruent corresponding angles and sides in proportion, making them similar. This means that option B is a possibility.
(C) A rectangle: Rectangles have four sides and four right angles. While two rectangles have congruent corresponding angles, they do not necessarily have sides in proportion. Therefore, option C is not the correct answer.
(D) A square: Squares are a type of rectangle, meaning they also have four sides and four right angles. All squares are rectangles, but not all rectangles are squares. Since squares have congruent corresponding angles and sides in proportion, option D is the correct answer.
(E) A trapezoid: Trapezoids have four sides, but their angles are not necessarily congruent. Additionally, it is unlikely for two trapezoids to have corresponding sides in proportion. Therefore, option E is not the correct answer.
Therefore, the correct answer is (D) square.