Question

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

Explanation:

Step1: Recall similarity criteria

Similarity of triangles can be established using transformations. Rigid transformations (like translations, rotations, reflections) preserve shape and size. Dilations change the size but not the shape.

Step2: Analyze equilateral triangles

All equilateral triangles have equal angles ($60^{\circ}$ each). To show similarity, we can use dilations (to adjust size) and rigid transformations (to adjust position/orientation).

Answer:

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