Are any two isosceles triangles similar? Are any two right triangles similar?

Triangles are similar if their angles are correspondingly equal and the similar sides are proportional.

Or, using the first sign of similarity, we will rely on two equal angles: If two angles of one triangle are equal to two angles of another triangle, then such triangles are similar.

1) Consider a counterexample: let the first triangle be acute-angled, has angles of 50 °, 50 ° and 80 °, the second triangle is obtuse – 20 °, 20 ° and 140 °. Such triangles cannot be alike! Therefore: no, any two isosceles triangles are not alike.

2) Similarly, for right-angled triangles. Yes, one of the angles is the same – 90 °, but the other two can be different. In the first it is 45 ° and 45 °, and in the second it is 60 ° and 30 °. There can be no similarity again. Therefore: no, any two right-angled triangles are not alike.