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.
