Which theorem states that in a right triangle, the squares of the legs sum to the square of the hypotenuse?

Which theorem states that in a right triangle, the squares of the legs sum to the square of the hypotenuse?

• A. Distance Formula
• B. Pythagorean Theorem
• C. Law of Sines
• D. Law of Cosines

Answer: (B)

In a right triangle, the lengths of the two legs relate to the hypotenuse by a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse. This means the sum of the squares of the two shorter sides equals the square of the longest side. It’s easy to see its power with a quick check: a 3-4-5 triangle satisfies 3^2 + 4^2 = 5^2 because 9 + 16 = 25. The Distance Formula uses the same squared-difference idea to measure distance between points, but that’s a broader tool, not the specific relationship inside a right triangle. The Law of Sines relates all sides to their opposite angles in any triangle, and the Law of Cosines generalizes the Pythagorean relation to any triangle (reducing to the familiar a^2 + b^2 = c^2 when the included angle is 90 degrees). The statement described is the Pythagorean Theorem.

In a right triangle, the lengths of the two legs relate to the hypotenuse by a^2 + b^2 = c^2, where a and b are the legs and c is the hypotenuse. This means the sum of the squares of the two shorter sides equals the square of the longest side. It’s easy to see its power with a quick check: a 3-4-5 triangle satisfies 3^2 + 4^2 = 5^2 because 9 + 16 = 25. The Distance Formula uses the same squared-difference idea to measure distance between points, but that’s a broader tool, not the specific relationship inside a right triangle. The Law of Sines relates all sides to their opposite angles in any triangle, and the Law of Cosines generalizes the Pythagorean relation to any triangle (reducing to the familiar a^2 + b^2 = c^2 when the included angle is 90 degrees). The statement described is the Pythagorean Theorem.