Question

if you draw 4 points in a square shape and try to join them all with non-crossing path you can do that, but if you draw 5 points in a shape of pentagon and try to join them it does not work. So, the question is how to prove using one of Euler's equation that its not possible to connect all 5 points with noncrossing path. He also told us that there's 5 vertices,9 edges and 6 faces.