Given : Parallelogram ABCD in which diagonals AC and BD intersect at M.

Prove : M is the mid-point of LN.

According to the properties of a parallelogram, the diagonals of a parallelogram bisect each other.

⇒ MD = MB

Also, ∠ADB = ∠DBN (∵ alternate angles)

And, ∠DML = ∠BMN (∵ vertically opposite angles)

Hence, by Angle Side Angle congruency,

Δ DML ≅ Δ BMN

By using Corresponding Parts of Congruent Triangles,

LM = MN

∵ M is mid - point of LN.

Hence, M is the mid-point of LN