# Is it possible to have a equilateral right triangle?

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 ${180}^{0}$.