Are all equilateral triangles similar?

Yes, all equilateral triangles are similar to each other. This is because they have all sides equal and all angles equal to 60°, satisfying the condition for similarity.

Reason

• For two triangles to be similar, corresponding angles must be equal and sides proportional.
• In equilateral triangles, all three angles are 60° and sides have equal ratios.

Proof

Let the sides of two equilateral triangles be a and b.

Then, a/b = a/b = a/b (all sides in the same ratio).

So, by AAA (Angle-Angle-Angle) and SSS (Side-Side-Side) similarity criteria, all equilateral triangles are similar.