Question

Is it possible to have a equilateral right triangle?

Answer 1

The answer is no. We can use a proof by contradiction.

Suppose a right triangle is equilateral. If the triangle is equilateral, then it also has three congruent angles. Therefore the measure of each of its angles is `90^0`. It follows that the sum of its angles is `270^0`, which contradicts the theorem stating that the sum of the angles of a triangle is always equal to `180^0`.

Therefore, our initial hypothesis that a right triangle is equilateral is false.