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 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)

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 .

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)

In the figure, diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar(DeltaAOD) = ar(Delta BOC).

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 quadrilateral ABCD, AM and CN are altitudes on diagonal BD drawn from A and C respectively .Prove that ar(ABCD)= 1/2 BD(AM+CN)

In the given figure ABCD is a cyclic quadrilateral in which AC and BD are its diagonals. If angle DBC = 55 ^(@) and angle BAC = 45 ^(@), find angle BCD.

ABCD is a rectangle AC is diagonal. Find the nature of DeltaACD . Give reasons.

In the given figure, ABC and DBC are two triangles on the same base BC. If AD intersects BC at O, show that (ar(ABC))/(ar(DBC))= (AO)/(DO) .

In the given figure, ABD is a triangle right angled at A and AC bot BD . Show that AC^(2)= BC*DC