Which of the following statements is true?
A. all trapezoids are similar
B.all isosceles triangles are the same
C.all rectangles are similar
D.all equilateral triangles are similar
C
The true statement is: D. all equilateral triangles are similar.
Explanation: An equilateral triangle is a triangle with all three sides of equal length. Similarity refers to figures that have the same shape but may have different sizes. Since all equilateral triangles have the same shape, they are considered similar.
To determine which statement is true, let's analyze each option:
A. All trapezoids are similar: This statement is false. Trapezoids can have different angles and side lengths, which means they can have different shapes and sizes. Hence, not all trapezoids are similar.
B. All isosceles triangles are the same: This statement is also false. Isosceles triangles have two equal side lengths and two equal angles. However, the lengths of the remaining sides and the size of the remaining angle can vary, resulting in different shapes and sizes. Therefore, not all isosceles triangles are the same.
C. All rectangles are similar: This statement is true. Rectangles have four right angles, and opposite sides are congruent. Therefore, all rectangles have the same shape, although they may differ in size.
D. All equilateral triangles are similar: This statement is also true. Equilateral triangles have three equal side lengths and three equal angles. Since all their angles and side lengths are the same, all equilateral triangles are similar to each other.
So, the correct answer is C. All rectangles are similar.