The two acute angles of the isosceles square are 45 °. Two identical isosceles right triangle rulers can form a square or a larger isosceles right triangle. The two right-angle sides of an isosceles square are equal in length.

There are two kinds of right-angle triangles, which are common right-angle triangles and isosceles right-angle triangles. In a right triangle, the two sides adjacent to the right angle are called right angles, and the side opposite the right angle is called hypotenuse. The right side of a right triangle is also called a "chord". If two right-angle sides are not the same length, the shorter side is called "hook" and the longer side is called "strand".