In a parallelogram ABCD, AX and CY are the bisectors of `angleAandangleC` respectively. Prove that `AX"||"CY.`

In the adjoining figure, ABCD is a parallelogram , AO and BO are the bisectors of angleA and angleB respectively. Prove that angleAOB=90^@ .

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

In parallelogram ABCD, X and Y are mid-points of opposite sides AB and DC respectively. Prove that: (i) AX=YC. (ii) AX is parallel to YC (iii) AXCY is a parallelogram.

In parallelogram ABCD, X and Y are mid-points of opposite sides AB and DC respectively. Prove that: (i)AX=YC (ii) AX is parallel to YC (iii)AXCY is parallelogram

ABCD is a parallelogram and line segments AX,CY bisects the angles A and C respectively show that AX||CY.

In the adjoining figure, BX and CY are the bisectors of angle ABC and angle ACB respectively. If AB=AC and BY=4 cm, then find the lengths of AX.

In the parallelogram ABCD ,M is mid-point of AC and X,Y are points on AB and DC respectively such that AX = CY. Prove that : (i) Triangle AXM is congruent to triangle (ii) XMY is a straight line.

ABCD is a parallelogram andline segments AX,CY biset the angles A and C, respectively Figure.Show that AX|CY Figure

If in DeltaABC bar(BX) and bar(CY) are bisectors to the base angles then angleBXC =

ABCD is a cyclic quarilateral. The bisectors of angleaandangleC in tersect the circle at the points E and F respectively . Prove that EF is a diameter of the circle.