In an equilateral triangle, all the sides are equal. If we use the longest side theorem which say in the triangle the longest side is across the largest angle. Since all the sides are equal then the angles must be equal too. So we can't have an Right angled equilateral triangle.

Why a right triangle Cannot be an equilateral triangle?

An equilateral triangle cannot have a right angle, which is 90∘ . All three angles in an equilateral triangle are 60∘ , and all three sides are the same length.

Are equilateral triangles right triangles?

Drawing the altitude of an equilateral triangle decomposes the equilateral triangle into 2 congruent triangles. They are right triangles with acute angles of 30 and 60 degrees. These congruent angles make all triangles with angles 30, 60, and 90 degrees similar by the Angle-Angle Triangle Similarity Theorem.