Question

In this problem, we're going to explain why any trapezoid that can be inscribed in a circle must be an isosceles trapezoid. In this 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.

Answer 1

Explanation:

"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.

Answer 2

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.