The line segments joining the midpoints M and N of parallel sides AB and DC respectively of a trapezium ABCD is perpendicular to both the sides AB and DC. Prove that AD=BC

Line segment joining the mid points M and N of parallel sides AB and DC, respectively of a trapezium ABCD is perpendicular to both the sides AB and DC. Prove that AD=BC.

In a cyclic trapezium ABCD,side AB is parallel to side DC. Prove that : side AD =side BC.

Prove that the line segment obtianed by joining the midpoints of two transversed sides of a trapezium is parallel to the parallel sides of the trapezium.

Prove that the line segment obtained by joining the midpoints of the diagonals of a trapezium is parallel to the parallel sides of the trapezium.

In a trapezium ABCD, the side AB is parallel to DC and the diagonals AC and BD meet at X. Prove that XA*XD = XB*XC .

ABCD is a trapezium with AB||DC . E and F are points on non-parallel sides Ad and BC respectively such that EF is parallel to AB (see the given figure). Show that (AE)/(ED)=(BF)/(FC) .

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

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

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

The following figure shows a trapezium ABCD in which AB is parallel to DC and AD= BC Prove that: angleADC= angleBCD