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

In the figure, ABCDE is a pentagon. A line through B parallel to AC meets DC produced at F. Show that (i) ar (ACB) = ar (ACF) (ii) ar (AEDF) = ar (ABCDE)

IN the figure, P is a point in the interior of a parallelogram ABCD. Show that (i) ar(APB) + ar(PCD) = 1/2 ar (ABCD) (ii) ar (APD) + ar(PBC) = ar(APB) + ar (PCD)

ABCD is a trapezium with AB || DC,. A line parallel to AC interseets AB at X and BC at Y. Prove that ar (ADX) = ar (ACY)

The side AB of a parallelogram ABCD is produced to any point P. A line through A and parallel to CP meets CB produced at Q and then parallelogram PBQR is completed . Show that ar (ABCD) = ar (PBQR)

In the figure, ABCD is a quadrilateral. AC is the diagonal and DE || AC and also DE meets BC produced at E. Show that ar(ABCD) = ar (DeltaABE).

In P is a point in the interior of a parallelogram ABCD. Show that (ii) ar (APD) + ar (PBC) = ar (APB) + ar (PCD)

Diagonals AC and BD of a quadrilateral ABCD each other at P. Show that ar (APB) xx ar (CPD) =ar (APD) xx ar (BPC)

In the given figure, diagonals AC and BD of quadrilateral ABCD interset at O such that OB = OD. If AB = CD, then show that : (i) ar (DOC) = ar (AOB) (ii) ar (DCB) = ar (ACB) (iii) DA || CB or ABCD is a parallelogram .

Diagonals AC and BD of a quadrilateral ABCD intersect each other at P. Show that ar (APB) xx ar (CPD) = ar (APD) xx ar (BPD). [Hint : From A and C, draw perpendiculars to BD.