ABCD is a quadrilateral in which AB = CD. Also, there is a point O inside the quadrilateral such that OA = OD and OB = OC.

State whether the statement regarding above information is true or false.

BC is parallel to AD.

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True

False

answer is A.

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Detailed Solution

Given, ABCD is a quadrilateral in which AB = CD.
Also, there is a point O inside the quadrilateral such that OA = OD and OB = OC.
Question Image

△ ABC

and

△ ODC

,
AB = CD (Given data)
OA = OD (Given data)
OB = OC (Given data)
Thus,

△ ABC ⩭ △ ODC

.[By SAS congruence rule].
Thus AB parallel CD.
ABCD is a parallelogram.
BC parallel AD.
So, the given statement is true and the correct option is 1.

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