ABCD is a trapezium with AB parallel to CD.LM is the line joining midpoints of AD and BC respectively.It is given that LM parallel to AB.Prove that __ LM=1/2(AB+DC) __

Dear Student!

Join AC and let P be the point of intersection of AC and LM.

In ΔADC, L is the mid point of AD and LP||DC. (Given)

∴ P is the mid point of AC. (Converse of Mid Point Theorem)

We know that, line joining the midpoint of any two sides of triangle is parallel to the third side and half of it.

In ΔABC, M and P are the mid points of side BC and AC respectively,

Adding (1) and (2), we get

Cheers!

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