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Q.

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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a

True

b

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 ImageIn △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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