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 squareABCD is a quadrilateral. M is the midpoint of diagonal AC and N is the midpoint of diagonal BD. Prove that : AB^(2)+BC^(2)+CD^(2)+DA^(2)=AC^(2)=AC^(2)+BD^(2)+4MN^(2).

ABCD is quadrilateral with AB parallel to DC. A line drawn parallel to AB meets AD at P and BC at Q. prove that (AP)/(PD) = (BQ)/(QC)

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

In the figure, ABCD is a cyclic quadrilateral in which DC produced to E and CF is drawn parallel to AB such that angleADC=80^(@) and angleECF=20^(@) , then BAD = ?

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

In the adjoing figure, squareABCD is a square. DeltaBCE on side BC and DeltaACF on the diagonal AC are similar to each other. Then, show that A(DeltaBCE)=(1)/(2)A(DeltaACF)

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 -