In a right triangle, which relation is true?

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

Answer: (A)

The key idea is the Pythagorean theorem: in a right triangle, the square of the hypotenuse equals the sum of the squares of the other two sides. If c is the hypotenuse and a and b are the legs, then a^2 + b^2 = c^2. This matches the given relation because it uses the two shorter sides and gives the square of the longest side as their sum. The other expressions would imply a different side is the longest (the hypotenuse) or would conflict with the basic properties of squares, so they don’t hold in a right triangle.