Geometry: Prove that DE = 2MN

[missa0312]

Given a triangle ABC, let M be the midpoint of side AB and N be the midpoint of side AC. Drop perpendiculars from B and C to the line MN; i.e. let D and E be on MN so that BD and CE are perpendicular to MN. Prove that DE=2MN.

 

[wjm11]

Given a triangle ABC, let M be the midpoint of side AB and N be the midpoint of side AC. Drop perpendiculars from B and C to the line MN; i.e. let D and E be on MN so that BD and CE are perpendicular to MN. Prove that DE=2MN.

Place point F as the midpoint of BC. Connect all the midpoints to form triangles. Does this suggest anything?