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const2013 [10]
3 years ago
11

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.

Mathematics
2 answers:
Softa [21]3 years ago
8 0

Step-by-step 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.

Triss [41]3 years ago
4 0

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.

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