Menelaus, an ancient Greek mathematician, first proved Menelaus theorem. It points out that if a straight line intersects with three sides AB, BC, CA of △ABC or its extension lines at points F, D and E, then (AF/FB )× (BD/DC )× (CE/EA) =1.

Evidence 1:

The passing point a is the extension line where AG‖BC intersects DF at g,

Then af/FB = ag/BD, BD/DC = BD/DC, ce/ea = DC/ag.

Multiply by three formulas: (AF/FB) × (BD/DC )× (CE/EA) = (AG/BD )× (BD/DC )× (DC/AG) =1.

Evidence 2:

If CP‖DF passes through AB to P at point C, BD/DC=FB/PF, CE/EA=PF/AF.

So there are AF/FB× BD/DC× CE/EA = AF/FB× FB/PF× PF/AF =1.