Question

Are two isosceles triangles always similar? Are two equilateral triangles always similar? Give reasons for your answers to both questions.

Answer 1

Isosceles triangles are not always similar, but equilateral triangles are always similar.

Explanation:

For two triangles to be similar the angles in one triangle must have the same values as the angles in the other triangle. The sides must be proportionate.

Both may be isosceles but one could have angles of `30°,30° 120°` and the other could have `20°20° 140°`
.
Hence it is not always true that isosceles triangles are similar.

For the equilateral triangles since they always have 3 angles that are each `60°`, any equilateral triangles will be similar.