If the diagonals of a quadrilateral bisect each other then quadrilateral is a parallelograms. Prove it

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Solution

R.E.F image In $△$ AOB & $△$ COD
AO=CO
$∠ A O B = ∠ C O P$
BO=DO
$∴$ $△ A O B ≅△ C O D b y S . A . S .$
Hence AB=CD (by cpct)
$∠ 1 = ∠ 2$
Hence $, A B | | C D$
Now in a quadrilateral
if me pair of opposite
side are equal & parallel
then it is a parallelograms
Thus,ABCD is a parallelograms proved.

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If the diagonals of a quadrilateral bisect each other then quadrilateral is a parallelograms. Prove it

R.E.F image In △ AOB & △ CODAO=CO∠AOB=∠COPBO=DO∴ △AOB≅△CODbyS.A.S.Hence AB=CD (by cpct)∠1=∠2Hence ,AB||CDNow in a quadrilateral if me pair of oppositeside are equal & parallelthen it is a parallelogramsThus,ABCD is a parallelograms proved.