Question

Why are isosceles right triangles similar?

Answer 1

Because all their angles are, correspondingly, congruent.

Explanation:

We are talking about right triangles with equal in length two catheti.
One angle, across the hypotenuse, is `90^o`. Two others must be equal since a triangle is isosceles, that is they are equal to `45^o` each.

So, any right isosceles triangle has angles `90^o`, `45^o` and `45^o`.
According to one of theorems of similarity, two triangles are similar if two angles of one correspondingly equal to two angles of another.