Which statement about a right triangle is commonly true and relates to the Pythagorean theorem?

• A. To compute the length of the diagonal in a square
• B. To determine the angle between two lines
• C. To verify that the square of the hypotenuse equals the sum of the squares of the legs in a right triangle
• D. To calculate the area of a triangle

Answer: (C)

Think of a right triangle with two shorter sides called legs and the longest side called the hypotenuse. The fundamental rule is that the square of the hypotenuse’s length equals the sum of the squares of the legs’ lengths. This is the Pythagorean theorem, so stating it this way directly expresses how the side lengths relate in any right triangle. It’s the best answer because it captures the exact relationship the theorem describes. For example, with legs 3 and 4, the hypotenuse is 5 since 3^2 + 4^2 = 9 + 16 = 25, and 5^2 = 25.

The other options involve related ideas but aren’t the central statement of the Pythagorean relationship: computing a diagonal in a square is a common application of the idea but not the general rule for right triangles, determining an angle between lines relies on angles and slopes, and calculating area uses a different formula altogether.