how to prove that the height of the medial triangle is half of the height of the original triangle????
+128475 
Let triangle EDF be medial, then AE = EC and that BD = DC
So....ED splits the sides AC and BC in the same proportion 1 : 1
So .....it is parallel to AB.....
And since AE =(1/2) AC and BD = (1/2) BC.....then ED =(1/2) AB
And by the same reasoning, we can show that EF =(1/2)BC and FD = (1/2) AC.....then triangles ABC and DEF are similar figures......and similar figures are similar in all respects.....so altitude of medial triangle DEF = (1/2) altitude of triangle ABC
