ABCD is a trapezium with AB || DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar (ADX) = ar (ACY). [Hint : Join CX.]

ABCD is trapezium in which AB||DC . DC is produced to E such that CE = AB, prove that ar(triangleABD) = ar(triangleBCE)

In a parallelogram ABCD, the bisector of /_A also bisects BC at X. Prove that AD = 2AB.

A line parallel to BC of a triangle ABC, intersects AB and AC at D and E respectively. Prove that (AD//DB) =( AE//EC) .

ABCD s a trapezium in which AB||CD and AD=BC diagonal AC=diagonal BD

ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that: ar(AEDF) = ar(ABCDE)

ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that: ar(ACB) = ar(ACF)

ABC is a right triangle such that AB=AC and bisector of angle C intersects the side AB at D. prove that AC+AD=BC.

P is the mid point of the side CD of a paralellogram ABCD, a line thorugh C parallelogram to PA intersects AB at Q and DA produced by A. Prove that DA=AR and CQ=QR.

ABCD is a trapezium in which AB II DC and its diagonals intersect each other at the point O. show that (AO)/(BO)=(CO)/(DO) .

The diagonals of a prallelogram ABCD intersect at O. A line through O intersets AB at P and DC at Q. prove that OP=OQ.