Final answer:
The correct step for Donna to use to prove that a triangle is right-angled is to apply the Pythagorean Theorem. She would compare the sum of the squares of the two shorter sides with the square of the longest side to confirm the triangle's right-angle nature.
Step-by-step explanation:
The correct answer for Donna to use as the third step in her outline of the proof to conclude that the triangle drawn is a right triangle is a) Use the Pythagorean Theorem. The Pythagorean Theorem states that in a right triangle, the sum of the squares of the two shorter sides (legs) is equal to the square of the longest side (hypotenuse). In other words, if we label the legs of the triangle as a and b, and the hypotenuse as c, then the theorem gives us the relationship a² + b² = c². This theorem is specific to right triangles, and proving this relationship is a definitive way to establish that a given triangle is a right triangle. As a step in an outline of a proof, applying the Pythagorean Theorem would involve squaring the lengths of what are suspected to be the legs of the triangle, adding these values together, and seeing if the result is equal to the square of the length of what is suspected to be the hypotenuse. If equality is established, this affirms the triangle is a right triangle.