Question

In a triangle ABC median ad is produced to x such that AD=DX .prove that ABXC is parallelogram. can we write that BD =DC (median) AD =DX (given) since the diagonals bisect each other ABXC is a parallelogram

Answer 1

BD = DC (D is the midpoint of BC)

 AD = DX(given)

Therefore the diagonals bisect each other , hence  it is a parallelogram .

Answer 2

yes . u r right.
 In triangle ABC, AD is median.
  Therefore, BD=DC....eqn1
   Also,AD=DX(Given)....eqn2
  Now, in quad. ABXC,
       AD=DX and BD=DC (Frm 1 & 2)
       Therefore, ABXC is parallelogram.(A quad. is a parallelogram if its diagonals bisect each other.)