In □ABCD, M and N are the mid-points of and . If ∥ prove that ∥

Given: In □ ABCD, M and N are the mid points ofand and ∥

To Prove: ∥

Construction:- extend towards D and towards C to intersect each other at P ( ∵ AB > CD)

Proof:- M is the mid-point of

∴ DA = 2 DM …………1

Similarly, N is the mid-point of

∴ CB = 2 CN…………..eq(2)

In Δ PAB , ∥

∴

( ∵ If a line ∥ to one side of a Δ intersects the other two sides of the Δ in distinct points, the segments of the other sides of the Δ in the same half plane of the line are proportional to the corresponding sides of the Δ)

∴ (from 1 and 2)

∴

In Δ PMN, P-D-M , P-C-N and

And

∴ ∥