Q. 35.0( 1 Vote )

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

Answer :


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



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