Which equation correctly expresses the Pythagorean theorem for a triangle where c is the hypotenuse and a and b are the legs?

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

Answer: (A)

In a right triangle, the squares of the legs combine to give the square of the hypotenuse. Since c is the hypotenuse and a and b are the legs, the correct relationship is c^2 = a^2 + b^2. You can also express it as a^2 + b^2 = c^2, which is the same idea written with the terms in the opposite order. Subtracting one leg’s square from the others doesn’t reflect the standard Pythagorean relationship for a right triangle.