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Question

In the below quadrilateral ABCD, if AD = BC and DAB = CBA, then what is the relation between ABD and BAC ?


A

ABD = BAC

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B

ABD < BAC

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C

ABD > BAC

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D

DAB = BAC

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Solution

The correct option is A

ABD = BAC


In ΔABD and ΔBAC,
AD = BC (Given)
BAD = CBA (Given)
AB = BA (Side common to both triangles)
Hence ΔABDΔBAC
(by SAS congruence condition).
Thus, ABD = BAC
(corresponding parts of congruent triangles).


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