Question

In Triangle ABC,Median AM is produced to D such that AM=MD. Prove that ABCD is a parallelogram.

Answer 1

Ans=
Given: ABC is a triangle.

AD is the median and producedvto P such that AD = DP.

Prove that ABCP is a parallelogram.

Proof: Since AD is a median, BD = CD

AD = DP [given]

ABCP is a quadrilateral and the lines AP and BC are diagonals.

The 2 diagonals are bisected by each other at D.

Hence ABPD is a parallelogram.

QED.