Question
Prove that the diagonals of a parallelogram bisect each other.
✓
Answer
Given: $||gm ABCD $ in which diagonals $AC$ and $BD$ bisect each other.
To Prove :$ OA = OC$ and $OB = OD$
Proof : $AB || CD ($Given$)$
$\angle 1 = \angle 2 ($alternate $\angle s)$
$\angle 3 = \angle 4 = ($alternate $\angle s)$
and $AB = CD ($opposite sides of $//gm)$
$\triangle COD = \triangle AOB (\text{A.S.A}.$ rule$)$
$OA = OC$ and $OB = OD$
Hence the result.
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