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

ABCD is a parallelogram. The diagonals AC and BD intersect each other at ‘O’. Prove that ar(DeltaAOD) = ar(DeltaBOC) . (Hint: Congruent figures have equal area)

ABCD is a cyclic quadrilateral. If AB = DC, then prove that AC= BD.

In a quadrillateral ABCD, it is given that AB ||CD and the diagonals AC and BD are perpendiclar to each other . Show that AD. BC = AB. CD.

ABCD is a cyclic quadrilateral such that AC bisects angleBAD . AD is produced to E in such a way that DE =AB . Prove that CE = CA .

In the figure, XY is a line parallel to BC is drawn through A. If BE || CA and CF || BA are drawn to meet XY at E and F respectively. Show that ar(DeltaABE) = ar (DeltaACF).

In the adjacent figure ABCD is a parallelogram and E is the midpoint of the side BC. If DE and AB are produced to meet at F, show that AF = 2AB .

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD. Show that AD = AE.

AB is a diameter of a circle. CD is a chord parallel to AB and 2CD = AB . The tangent at B meets the line AC produced at E then AE is equal to -