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

In DeltaABC , the bisectors of angleB and angleC intersect each other at O. Prove that. angleBOC=90^(@)+(1)/(2)angleA .

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

In parallelogram ABCD, the bisectors of /_A and /_B intersect at M. If /_A = 80^(@) , then /_AMB=…….

In triangleABC the bisectors of angleB and angleC intersect at I if angleA=70^(@) then angle BIC=…………..

In quadrilateral ABCD, the bisectors of /_A and /_B intersect at E. Prove that, /_C+ /_D = 2/_ AEB.

In triangle ABC, the bisectors of angle B and angle C intersect at I. A line drawn through I and parallel to BC intersects AB at P and AC at Q. Prove that PQ = BP + CQ.

In a parallelogram ABCD, E and F are the midpoints of the sides AB and DC respectively. Show that the line segments AF and EC trisect the diagonal BD.

In triangle ABC, AB = AC and the bisector of angle A lt intersects BC at D. Prove that, ( 1 ) triangle ADB = triangle ADC ( 2 ) angle ABC = angle ACB

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 .

Show that the bisectors of angles of a parallelogram form a rectangle.