State the Pythagorean theorem for a right triangle with legs a and b and hypotenuse c.

State the Pythagorean theorem for a right triangle with legs a and b and hypotenuse c.

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

Answer: (A)

In a right triangle, the length of the hypotenuse is closely tied to the squares of the two legs: the square on the hypotenuse equals the sum of the squares on the legs. With legs a and b and hypotenuse c, that gives a^2 + b^2 = c^2. The other forms don’t match this relationship (they either subtract squares or mix the terms in ways that don’t correspond to the triangle’s side lengths). So the correct expression is a^2 + b^2 = c^2.

In a right triangle, the length of the hypotenuse is closely tied to the squares of the two legs: the square on the hypotenuse equals the sum of the squares on the legs. With legs a and b and hypotenuse c, that gives a^2 + b^2 = c^2. The other forms don’t match this relationship (they either subtract squares or mix the terms in ways that don’t correspond to the triangle’s side lengths). So the correct expression is a^2 + b^2 = c^2.