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

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

In the given figure, angleB lt angleA and angleC lt angleD . Show that AD lt BC .

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

Diagonal AC of a parallelogram ABCD bisects A. Show that it bisects C also

Diagonals AC of a parallelogram ABCD bisects angleA . Show that it bisects angleC also ABCD is a rhombus

In an isosceles ABC, with AB = AC, the bisectors of angleB and angleC intersect each other at O. Joint A to O. Show that: (ii) OB = OC (ii) AO bisects angleA

In a parallelogram ABCD, E and F are the mid points of sides AB and CD respectively (see fig.) Show that the line segements AF and EC trisect the diagonal BD.

Diagonal AC of a parallelogram ABCD bisects A. Show that ABCD is a rhombus.

Throught the mid-point M of the sides of a parallelogram ABCD, the line BM is drawn intersecting AC at L, and AD produced to E. Prove that EL = 2 BL .

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 .