In a quadrilateral ABCD the linesegment bisecting `angleC and angleD` meet at E. Prove that `angleA+angleB=2angleCED.`

In a quadrilateral ABCD, AO and BO are bisector of angle A and angle B resepectively. Sho that : angleAOB=1/2 (angleC+angleD)

Find angleA+angleB+angleC+angleD

In quadrilateral ABCD, AB is the shortest side and DC is the longest side. Prove that : (i) angleB gt angleD (ii) angleA gt angleC

If bisectors of angleA and angleB of a quadrilateral ABCD intersect each other at P, of angleB and angleC at Q, of angleC and angleD of R and of angleD and angleA at S, then PQRS is a (A) Rectangle (B) Rhombus (C) Parallelogram (D) Quadrilateral whose opposite angles are supplementary

In a parallelogram ABCD, the bisectors of angleA and angleB intersect each other at point P. Prove that angleAPB=90^(@).

Bisectors of angles A and D of a quadrilateral ABCD meet at P. Prove that angleAPD=(1)/(2)(angleB+angleC)

In the adjoining figure, AB gt AC and the angle bisectors of angleB and angleC meet at point P. Prove that PB gt PC .

If the diagonal BD of a quadrillateral ABCD bisects both angleB and angleD . Prove that (AB)/(BC)= (AD)/(CD) .

In parallelogram ABCD, the bisector of angle A meets DC at P and AB= 2AD. Prove that: BP bisects angle B

In a cyclic quadrilateral ABCD the diagonal AC bisects the angle BCD. Prove that the diagonal BD is parallel to the tangent to the circle at point A.