AB and CD are the parallel sides of a trapeziuml. E is the mid-point of AD. A line through E and parallel to side AB meets the line BC at point F. Prove that F is the mid-point of BC.

In a trapezium ABCD, AB/DC, E is mid-point of aD. A line through E and parallel to AB intersects BC at point F. Show that: 2EF=AB+DC

E is the mid-point of the side AD of the tarapezium ABCD with AB||DC . A line through E drawn parallel to AB intersects BC at F. Show that F is the mid-points of BC.

ABCD is a trapezium in which A B\ ||\ D C , BD is a diagonal and E is the mid-point of AD. A line is drawn through E parallel to AB intersecting BC at F (see Fig. 8.30). Show that F is the mid-point of BC.

D and F are the mid-points of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E. Prove that BDFE is a parallelogram

In parallelogram ABCD, E is the mid-point of AB and AP is parallel to EC which meets DC at point O and BC produced at P. Prove that: O is mid-point of AP.

In a triangle ABC, AD is a medium and E is mid-point of median AD. A line through B and E meets AC at point F.

D and F are the mid-points of sides AB and AC of a triangle ABC. A line through F and parallel to AB meets BC at point E. Find AB, if EF=4.8cm .

The diagonals AC and BD of a cyclic quadrilateral ABCD interest at right angles at E (figure). A line l drawn through E and perpendicular to AB meets CD at F. Prove that F is the mid-point of CD.

In Figure, A B C D isa trapezium in which side A B is a parallel to side D C and E is the mid-point of side A D . If F is a point on the side B C such that the segment E F is parallel to side D C . Prove that F is the mid point of B C and E F=1/2(A B+D C) .

ABC is a triangle right angled at C and M is mid-point of hypotenuse AB. Line drawn through M and parallel to BC intersects AC at D. Show that: MD is mid-point of AC.