Answered: Suppose that AB = BC, ∠BAD = ∠BCD, and…

Suppose that AB = BC, ∠BAD = ∠BCD, and that the line AC bisects ∠BAD. Prove that ABCD is a rhombus, i.e., all four sides have equal length and both pairs of opposite sides are parallel.

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter7: Locus And Concurrence

Section7.1: Locus Of Points

Problem 40E

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Question

Suppose that AB = BC, ∠BAD = ∠BCD, and that the line AC bisects ∠BAD. Prove that ABCD is a rhombus,
i.e., all four sides have equal length and both pairs of opposite sides are parallel.

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