The Pythagorean theorem expresses a relationship between which elements of a right triangle?

• A. Two legs and a vertex
• B. One leg and the hypotenuse
• C. Two legs and the hypotenuse
• D. Three sides and a height

Answer: (C)

The Pythagorean theorem relates the lengths of the sides of a right triangle: the two legs and the hypotenuse. If you call the legs a and b and the hypotenuse c, then a^2 + b^2 = c^2, showing that the sum of the squares of the legs equals the square of the hypotenuse. The hypotenuse is the side opposite the right angle and is the longest side, which is why it appears in the equation with the two legs. The vertex is a point, not a side, so it doesn’t appear in the relationship. The height is a separate geometric measure used for area, not part of the standard Pythagorean relationship. For example, a 3-4-5 triangle satisfies 3^2 + 4^2 = 5^2, illustrating the connection between the two legs and the hypotenuse.