In a right triangle, the Pythagorean theorem states that the sum of squares of the legs equals the square of the hypotenuse. Which equation represents that relation?

In a right triangle, the Pythagorean theorem states that the sum of squares of the legs equals the square of the hypotenuse. Which equation represents that relation?

• A. a^2 = b^2 + c^2
• B. c^2 = a^2 + b^2
• C. a^2 + b^2 = c^2
• D. a^2 + c^2 = b^2

Answer: (C)

Pythagorean theorem in a right triangle: the square of the hypotenuse equals the sum of the squares of the two legs. If we call the legs a and b and the hypotenuse c, the relationship is a^2 + b^2 = c^2. This matches the described statement directly—the sum of the squares of the legs equals the square of the hypotenuse. It’s also common to write it as c^2 = a^2 + b^2, which is the same equation rearranged. For a concrete check, in a 3-4-5 triangle we have 3^2 + 4^2 = 9 + 16 = 25, and 5^2 = 25, which confirms the pattern. The other forms would place the hypotenuse on the wrong side or swap which side is squared, which doesn’t reflect the right-triangle setup.

Pythagorean theorem in a right triangle: the square of the hypotenuse equals the sum of the squares of the two legs. If we call the legs a and b and the hypotenuse c, the relationship is a^2 + b^2 = c^2. This matches the described statement directly—the sum of the squares of the legs equals the square of the hypotenuse. It’s also common to write it as c^2 = a^2 + b^2, which is the same equation rearranged. For a concrete check, in a 3-4-5 triangle we have 3^2 + 4^2 = 9 + 16 = 25, and 5^2 = 25, which confirms the pattern. The other forms would place the hypotenuse on the wrong side or swap which side is squared, which doesn’t reflect the right-triangle setup.