in a parallelogram ABCD ,the bisector of angle A also bisect BC at X.prove that AD=2AB

This could not be possible because the angle bisectors of angle A will be its diagonal so it could not cut BC at X.

in paralleloram abcd

since AX is the bisector of ang. A 

so, ang.DAX=ang.AXB    .............1                        (ALTERNATE ANGLES)

SO, 

in triangle AXB 

ang.BAX=angAXB                      frm 1 

SO, ab = bx  ..............2

so ad=2bx 

sso ad=2ab                              frm2

hence proved 

this is not possible at all... because when any ine bisect angle A, then it can't bisect line segment BC ... and if it is so ... then it wil b a curve not a line.....

use similaity in it