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Question 334397: Which of the following are always similar? Why?
a. Any two equilateral triangles
b. Any two squares
c. Any two rectangles
d. Any two rectangles in which one side is twice as long
as the other.
Answer by nyc_function(2741)   (Show Source):
You can put this solution on YOUR website! a: Recall the definition of similarity for triangles. Two triangles are similar if they have the same angles and the side lengths are proportional. Since equilateral triangles all have the same angles, and all side lengths are equal, any two equilateral triangles must be similar.
b. Always similar. All side lengths are the same, and therefore must be proportional to the lengths of any other square.
c. No. The ratio of side lengths can take on any value for arbitrary rectangles. They do not have to be similar.
d. Yes. The ratio of the side lengths is consistent, and so the rectangles are similar.
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