Which best explains why all equilateral triangles are similar?

a. all equilateral triangles can be mapped onto each other using dilations.

b. all equialeratl triangles can be mapped onto each other using rigid transformations

c. all equilateral triangles can be mapped onto each other using combo of dilations and rigid transformations.

d. all equilateral triangles are congruent and therefore similar, with side lengths in a 1:1 ratio

(a) option is correct.

Step-by-step explanation:

Equilateral triangles have all the three sides of equal length and all the three angles equal to 60 degree.

Only thing which can be changed in an equilateral triangle is the length of the sides.

Moreover, dilation is a transformation used to change the size of the figure via some scale or number.

So, when dilation is applied on an equilateral triangle, its size can be made small or large as per the requirement.

Hence, equilateral triangles can be mapped onto each other using dilations.