All equilateral triangles are similar because they have the same shape, even if their sizes differ. Here’s why:
- Equal Angles: Every equilateral triangle has three angles that each measure 60 degrees. Since the angles are identical, the triangles are similar by the Angle-Angle (AA) similarity criterion.
- Equal Side Lengths: In an equilateral triangle, all three sides are of equal length. This means that the ratio of corresponding sides in any two equilateral triangles is always the same, which is another condition for similarity.
Because both the angles and the side ratios are the same in all equilateral triangles, they are guaranteed to be similar to each other regardless of their size.