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).`

The sides AB and AC are equal of an isosceles triangle ABC. D E and F are the mid-points of sides BC, CA and AB respectively. Prove that: (i) Line segment AD is perpedicular to line segment EF. (ii) Line segment AD bisects the line segment EF.

In trapezium ABCD, AB is parallel to DC. P and Q are the mid-points of AD and BC respectively. BP produced meets CD produced at point E. Prove that : PQ is parallel to AB.

In trapezium ABCD, AB is parallel to DC. P and Q are the mid-points of AD and BC respectively. BP product meets CD produced at point E. Prove that : Point P bisects BE,

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.

ABCD is a quadrilateral in which AD = BC. E, F, G and H are the mid-points of AB, BD, CD and AC respectively. Prove that EFGH is a rhombus.

The following figure shows a trapezium ABCD in which AB // DC. P is the mid-point of AD and PR // AB. Prove that: PR = (1)/(2)(AB + CD)

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. Show that (A E)/(E D)=(B F)/(F C) .

In Delta ABC, D,E and F are mid-point of sides AB ,BC and AC respectively , Prove that AE and DF bisect each other.

In Delta ABC, AB = AC. D , E and F are mid-points of the sides BC, CA and AB respectively . Show that : AD is perpendicular to EF.