Final answer:
Reflecting right triangle ABC across line BC creates triangle ACA', where AB = A'B = r, and AC is the base. This results in an isosceles triangle ACA' because it has two equal sides and a base that differs in length.
Step-by-step explanation:
Reflecting a right triangle ABC across the line BC implies that point A would be reflected to a point A' such that AA' is perpendicular to BC and AB is equal to A'B. Since AB = BC = r in right triangle ABC, and we are reflecting across BC, triangle ACA' is formed by joining the original position of A to its reflected counterpart A'. This new triangle is isosceles because AB = A'B = r, and the base AC remains unchanged.
Triangle ACA' has two sides of equal length, r, and one side of a different length, which doesn't change because AC is a side of the original triangle ABC. Therefore, triangle ACA' is classified based on its side lengths as an isosceles triangle.