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.

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

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.

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

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.

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 .

In triangle ABC, D and E are mid-points of the sides AB and AC respectively. Through E, a straight line is drawn parallel to AB to meet BC at F. Prove that BDEF is a parallelogram. If AB = 16 cm, AC = 12 cm and BC = 18 cm, find the perimeter of the parallelogram BDEF.

In the following figure, F and E are points on the side AD of the triangle ABD. Through F a line is drawn parallel to AB to meet BD at point C . Prove that : ar (Delta ACE ) = ar (quad . BCEF )

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.

O is the point of intersection of the diagonals AC and BD of a trapezium ABCD with AB abs() DC. Through O , aline segment PQ is drawn parallel to AB meeting AD in P and BC in Q, prove that PO=QO.