Which statement expresses the Pythagorean theorem for a right triangle?

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

Answer: (A)

In a right triangle, the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides. If you call the legs a and b and the hypotenuse c, the relationship is a^2 + b^2 = c^2. This equality is exactly the Pythagorean theorem.

The other expressions don’t express the same idea: a^2 + b^2 > c^2 would indicate the triangle is acute, a^2 + b^2 < c^2 would indicate an obtuse triangle, and a^2 - b^2 = c^2 isn’t the standard side-length relationship for a right triangle. This equality is specific to right triangles.