Which best explains why all equilateral triangles are similar?

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

Option 1 is true.

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

Step-by-step explanation:

Two figures that have the same shape are said to be similar. When two figures are similar, the ratios of the lengths of their corresponding sides are equal.

1)

As in a dilation the figure either shrink or expand by some factors so the ratio of the corresponding sides of both the triangle will have the same ratio.

Hence the triangle will be similar.

2)

All equilateral triangle can be mapped onto each other using the rigid transformation.

in rigid transformation such as reflection, rotation and translation and there combinations the location of shape of the figure might appear different.

Hence we could not say that they are similar.

3)

All equilateral triangles can be mapped onto each other using combinations of dilations and rigid transformations.

Same as in part 2) ; here also we may not obtain similar triangles.

4)

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

It is not necessary that the location of shape of two triangle might be same.

Hence, option 1 is true.