What defines a 'right triangle'?

A triangle is defined as a right triangle if it has one angle that measures exactly 90 degrees. This specific angle creates a unique set of properties, such as the relationship between the lengths of the sides, known as the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In contrast, the other options do not accurately describe a right triangle. A triangle with all angles equal would be an equilateral triangle, which does not have a right angle. A triangle with no equal sides is referred to as a scalene triangle, which may or may not be a right triangle. Lastly, a triangle with one obtuse angle is defined as an obtuse triangle, which has a different geometric classification altogether. Thus, the defining characteristic of a right triangle is the presence of a 90-degree angle.