Question

$\text{Given : Parallelogram ABCD in which diagonals AC and BD intersect at M.}\text{Prove : M is mid-point of LN.}$

Answer 1

$\text{Proof :~Diagonals of}|\text{gm bisect each other.}\therefore MD=MBAlso\angle ADB=\angle DBN\left(\text{Alternate}\angle s\right)\&\angle DML=\angle BMN\left(\text{Vert.opp.}\angle s\right)\therefore \Delta DML=\Delta BMN\therefore LM=MN\therefore \text{M is mid-point of LN.}\text{Hence proved.}$