If a quadrilateral ABCD, the bisector of `angleC angleD` intersect at O.
Prove that `angleCOD=(1)/(2)(angleA+angleB)`

In a parallelogram ABCD, the bisectors of the consecutive angles angleA and angleB intersect at P. Show that angleAPB=90^(@) .

In a quadrilateral AB|\|CD the diagonals intersect at ‘O’. Then S.T. /_\OAB ~ /_\OCD .

In a Quadrilateral ABCD, angleA +angleB = 200^@ then angleC +angleD = _____

In an isosceles triangle ABC, with AB =AC, the bisectors of angleB and angleC intersect each other at 'O'. Join A to O. AO bisects angleA

In a quadrilateral ABCD, angleB = 90^0 , AD^2 = AB^2 + BC^2 + CD^2 . Prove that angle ACD = 90 ^0 .

If the bisector of an angle of a triangle also bisects the opposite side, prove that the triangle is isosceles.

In the given figure angleA= 40^(@) . If bar(BO) and bar(CO) are the bisectors of angleB and angleC respectively. Find the measure of angleBOC .

Given that the vertices A, B, C of a quadrilateral ABCD lie on a circle. Also angleA + angleC = 180^@ , then prove that the vertex D also lie on the same circle.

The diagonals of a quadrilateral ABCD intersect each other at point'O' such that (AO)/(BO)=(CO)/(DO) . Prove that ABCD is a trapezium.