What is a right triangle?

• A. A triangle containing a 90º angle.
• B. A triangle with all sides equal.
• C. A triangle with no right angles.
• D. A triangle with two obtuse angles.

Answer: (A)

A right triangle is defined by having one angle that measures exactly 90 degrees. That right-angle feature sets it apart and determines its usual naming: the side opposite the 90-degree angle is the longest and is called the hypotenuse, while the other two sides are the legs. The two non-right angles always add up to 90 degrees, so the triangle’s angles total 180 degrees.

This shape is the backbone for the Pythagorean theorem, which says the squares of the legs add up to the square of the hypotenuse (a^2 + b^2 = c^2). It’s also the starting point for basic trigonometry with ratios like sine, cosine, and tangent that relate the angles to the sides.

In contrast, a triangle where all sides are equal is an equilateral triangle and has no right angle. A triangle with no right angles could be acute or obtuse, depending on whether all angles are less than 90 degrees or one angle is greater than 90 degrees. You can’t have two obtuse angles in a triangle because that would exceed 180 degrees in total.