Question

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.

Explanation:

Similar figures can be mapped to each other via a combination of rigid transformations (which preserve shape and size) and dilations (which preserve shape but change size proportionally). Equilateral triangles all have 60° angles, so their corresponding angles are congruent, and their sides are in proportional ratios. Rigid transformations alone only work for congruent triangles, not all similar ones (since equilateral triangles can be different sizes). Dilations alone can change size but may need rigid transformations to align orientation. Not all equilateral triangles are congruent (they can have different side lengths), so the correct reasoning involves combining dilations and rigid transformations.

Answer:

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