In this problem, we're going to explain why any trapezoid that can be inscribed in a circle must be an isosceles trapezoid. In t
his figure, let's assume without loss of generality that segments AB and DC are parallel. By the end of this problem, we want to show that ∠D ≅ ∠C. 1. Explain why ∠A must be supplementary to ∠D.
The single reason for <A and <D being supplementary is the fact that the segment AB is parallel to the segment CD in any trapezoid, so line AD is a transversal with corresponding angles <D and 180-<A congruent which implies <D and <A are supplementary, which answers the question.
Since the trapezoid can be inscribed in a circle, that means angle B + angle D = 180 degree. Since AB is parallel to CD, then angle B + angle C = 180 degree. Therefore, angle D = angle C.
When the lines are parallel then there is no solution to the system of equations. This happens because the intersection is the solution. And when there is no intersection then there is no solution.
