Mathematics
In the figure (i) given below, ABDC is a cyclic quadrilateral. If AB = CD, prove that AD = BC.
Circles
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Answer
Join AC and BD.
In △ABD and △CBD,
AB = CD (Given)
BD = BD (Common side)
∠BAD = ∠BCD (∵ angles in same segment are equal.)
∴ △ABD ≅ △CBD. (By SSA axiom of congruency.)
∴ BC = AD (As corresponding parts of congruent triangles are congruent.)
Hence, proved that BC = AD.
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