Question

In a triangle AC median AD is produced to X such that AD=DX . prove that  ADXC is a parallelogram

Answer 1

I am quite sure you meant Triangle ABC
also i believe that you are referring to ABXC as a parallelogram

We must use the property  of  a parallelogram where diagonal bisect each other..

Look in the figure below we have 

$AD = DX$ (FROM DATA){ONE SET OF DIAGONALS}

Now  AD is the median

∴ BD = CD

Now from the above 2 equation we gaet the diagonals bisect each other hence it is a parallelogram