Which equation represents the Pythagorean Theorem in a right triangle?

Which equation represents the Pythagorean Theorem in a right triangle?

• A. a^2 + b^2 = c^2, where c is the hypotenuse.
• B. a + b = c
• C. c^2 = a^2 - b^2
• D. a^2 + b^2 + c^2 = 0

Answer: (A)

In a right triangle, the squares of the two legs add up to the square of the hypotenuse. If the legs are a and b and the hypotenuse is c, then a^2 + b^2 = c^2. This is the form shown, with c identified as the hypotenuse. For example, in a 3-4-5 triangle, 3^2 + 4^2 = 9 + 16 = 25 = 5^2, illustrating the relationship directly. The other expressions don’t match this geometric rule: adding the side lengths (a + b = c) ignores the squaring; c^2 = a^2 - b^2 would imply subtracting squares; and a^2 + b^2 + c^2 = 0 cannot hold for positive side lengths.

In a right triangle, the squares of the two legs add up to the square of the hypotenuse. If the legs are a and b and the hypotenuse is c, then a^2 + b^2 = c^2. This is the form shown, with c identified as the hypotenuse. For example, in a 3-4-5 triangle, 3^2 + 4^2 = 9 + 16 = 25 = 5^2, illustrating the relationship directly. The other expressions don’t match this geometric rule: adding the side lengths (a + b = c) ignores the squaring; c^2 = a^2 - b^2 would imply subtracting squares; and a^2 + b^2 + c^2 = 0 cannot hold for positive side lengths.