E is any point on the side BC of the parallelogram ABCD. AE intersects the diagonal BD at point F. Prove that `DF×EF=FB×FA`.

E is a point on the side AD produced of a parallelogram ABCD and BE intersects CD at F. Show that triangleABE~triangleCFB .

M is the mid point of the side CD of the parallelogram ABCD. The line BM is drawn intersecting AC in L and AD produced Prove that (i) ALxxLM=CLxxBL

M is the mid point of the side CD of the parallelogram ABCD. The line BM is drawn intersecting AC in L and AD produced at E.Prove that(ii) EL = 2BL

ABCD is a parallelogram. E is the middle point of the side CD. BE intersects AC at the point X. prove that AX=2/3AC .

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 parallelogram. E is any point on the side BC, line segment drawn through D and E cards the extended AB at T Prove that DE * EB = CE * TE .

E is the mid point of the side AB of the square ABCD, if /_AED = theta then find the value of cos theta and sin theta .

triangleBAC and triangleBDC are two right-triangle on the same side of the base BC.If AC ans DB intersect each other at a point P,show that APxxPC=DPxxPB .

The sides of the quadriIateraI ABCD are not equal to one another and AC_|_BD prove that AB^2+CD^2=AD^2+BC^2

E is the middle point of the median AD of /_\ABC . BE intersects AC at F. Prove that AF=1/3AC .