Which equation expresses the Pythagorean theorem?

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

Answer: (A)

In a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. The expression that shows this relationship is c^2 = a^2 + b^2, with c as the hypotenuse and a and b as the legs. This form exactly captures the theorem: squaring the hypotenuse and adding the squares of the legs gives a true equality. The other options misrepresent the relationship: using a^2 = b^2 + c^2 would make a the hypotenuse, c = a + b wrongly suggests the hypotenuse is the sum of the legs, and a^2 + b^2 = c would imply c is not squared, which doesn’t reflect the theorem.