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

In the parallelogram ABCD , AP and DP are the bisectors of the angleBAD and angleADC respectively. Find the angleAPD

The bisector of the interior angles angleB and angle C of the DeltaABC , meet at H. Prove that angleBHC=90^@+(1)/(2)angleBAC .

In the parallelogram ABCD , AB = 2AD . Prove that the bisectors of the angles angleBAD and angleABC meet at the mid-point of DC at right -angles.

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

ABCD is a cyclic quadrilateral .The side BC is extended to E .The bisectors of the angles angleBADandangleDCE intersect at the point P .Prove that angleADC=angleAPC .

Delta ABC is inscirbed in a circle, the bisector of the angles angle BAC, angle ABC and angle ACB intersect at the point X,Y,Zon the circle repectively. Prove that in Delta XYZ , angle YXZ=90^(@)-(1)/(2) angle BAC

In a parallelogram ABCD, angleDAB = 40^(@) find the other angles of the parallelogram.

The perpendicular bisector of the three sides of a right - angled triangle intersect each other

Construct the bisector of a given angle /_ ABC=90^@ .