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CBSE Class 9 Answered

Prove that if the diagonals of a quadrilateral bisect each other, then it is a parallelogram.
Asked by Topperlearning User | 04 Jun, 2014, 01:23: PM
answered-by-expert Expert Answer

OA = OC and OB = OD [Given]

AOB = DOC [vertically opp. angles]

[SAS congruence]

Therefore ABO = CDO (cpct)

From this, we get AB||CD ...(i)

Similarly BC||AD ...(ii)

From (i) and (ii) ABCD is a ||gm.

Answered by | 04 Jun, 2014, 03:23: PM
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