1. The problem asks us to evaluate the reasoning of two students proving the Pythagorean Theorem for a right triangle with legs 5 cm and 12 cm. 2. The Pythagorean Theorem states that in a right triangle, the square of the hypotenuse $c$ equals the sum of the squares of the legs $a$ and $b$: $$c^2 = a^2 + b^2$$ 3. Student A calculates: $$5^2 + 12^2 = 25 + 144 = 169$$ and notes that $169 = 13^2$, so the hypotenuse $c = 13$ cm. 4. Student B incorrectly states that the hypotenuse is the sum of the legs: $$5 + 12 = 17$$ and claims the hypotenuse is 17 cm. 5. Student A correctly applies the Pythagorean Theorem by squaring the legs and summing them. 6. Student B incorrectly adds the legs directly without squaring, which is not how the hypotenuse is found. 7. Therefore, the best evaluation is: **A. Student A is correct, while Student B incorrectly used addition instead of squaring.**