Question

Which best explains why all equilateral triangles are similar?

A. All equilateral triangles can be mapped onto each other using dilations.
B. All equilateral triangles can be mapped onto each other using rigid transformations.
C. All equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations.
D. All equilateral triangles are congruent and therefore similar, with side lengths in a 1:1 ratio.

Answer 1

I think it is D. Due to the fact that all equilateral triangles have all the sides of the same length, giving it a ration of 1:1

Answer 2

Answer: A. All equilateral triangles can be mapped onto each other using dilations.

Explanation:

We know that all equilateral triangles are similar to each but not congruent because they all have same measure of corresponding angles 60° but do not have same side-lengths.

So, equilateral triangles can be mapped onto each other using dilation because they maps similar shapes (sometimes congruent) where as rigid transformations always map congruent shapes so we cannot map all equilateral triangles by using rigid transformations.