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

Question

Claire Akin · Accepted Answer

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

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.

Savannah Aguilar · Answer

undefined Two isosceles triangles are not always similar. Similarity of triangles depends on having proportional corresponding sides. Isosceles triangles have two sides of equal length, but the third side may vary in length. Therefore, if the third side of one isosceles triangle is different from the third side of another isosceles triangle, they will not be similar.

On the other hand, two equilateral triangles are always similar. This is because equilateral triangles have all three sides of equal length and all three angles equal to 60 degrees. Since all corresponding sides and angles are congruent, any two equilateral triangles will be similar.

Carson Arnold · Answer

undefined Two isosceles triangles are not always similar because they may have different angles. However, two equilateral triangles are always similar because they have equal angles.