In a trapezium ABCD, if E and F be the mid-points of diagonal AC and BD respectively. Prove that `EF=1/2(AB-CD).`

ABCD is a trapezium, in which AD||BC, E and F are the mid-points of AB and CD respectively, then EF is:

In a parallelogram ABCD, E and F are the mid-points of sides AB and CD respectively. Show that the line segments AF and EC trisect the diagonal BD.

In a parallelogram ABCD, E and F are the mid-points of sides BC and AD respectively. Show that the line segment BF and ED trisect the diagonal AC.

In the given figure ABCD is a trapezium with AB || DC. E and F are respectively midpoint of AD and BC. Prove that, EF=1/(2)(AB+CD)

If ABCD is quadrilateral and E and F are the mid-points of AC and BD respectively, prove that vec AB+vec AD+vec CB+vec CD=4vec EF

In Figure,ABCD is a parallelogram.E and F are the mid-points of the sides AB and CD respectively.Prov that the line segments AF and CE triset (divide into three equal parts) the diagonal BD.

If M and N are the mid-points of the diagonals AC and BD respectively of a quadrilateral ABCD,then the of vec AB+vec AD+vec CB+vec CD equals

In a trapezium ABCD,P and Q are points on AD and Bc respectively such that (DP)/(AP)=(CQ)/(BQ)=(1)/(3) .If the diagonal BD intersects PQ at E,find the ratio of ar DeltaDPE toarea of trapezium ABCD.