# Median length theorem

Submitted by Structure on Sat, 12/29/2007 - 18:25.

Let ABC a triangle and a=length(BC),b=length(CA),c=length(AB).

Let M be the middle of BC and D symmetric of A with respect of M.

Then ABDC is a parallelogram.

From cosine theorem we have

In triangle ABD we have

Summing up we have

Finally