Final answer:
The correct step used to prove BC^2 = AB^2 + AC^2 applies the Pythagorean Theorem and the distributive property, but the right option can only be determined with additional context or a diagram illustrating the relationship between the segments AB, AC, BC, BD, and DC.
Step-by-step explanation:
To find which step is used to prove that BC^2 = AB^2 + AC^2 in a right triangle, we need to identify the correct application of the Pythagorean Theorem which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be represented as a² + b² = c² where c is the length of the hypotenuse, and a and b are the lengths of the other two sides.
The correct option that applies the Pythagorean Theorem and the distributive property of multiplication over addition correctly is (b) By distribution, AC^2 plus AB^2 = BC multiplied by the quantity DC plus BD. However, based solely on the options provided and without additional context or a diagram, it is not possible to determine the exact relationship between AB, AC, BC, BD, and DC, as these would typically refer to particular segments in a diagram of a triangle or a related shape. Usually, BC would be the hypotenuse, AB and AC would be the other two sides of the right triangle, and DC and BD do not necessarily have a clear relationship with these sides without further context.