Question on convex pentagons with lattice points as its vertices
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I have the following question which I found as an example in a book with me: "All vertices of a convex pentagon are lattice points, and its sides have integral length. Show that its perimeter is even" The book starts the solution like this: "Colour the lattices as in a chess board and erect right triangles on the sides of the pentagon with the sides of the pentagon as the longest side. With the other two sides along the sides of the square trace the ten shorter sides. Since at the end we return to the point we started we must have traced an even number of lattice points." How is the last statement concluded?
graph-theory
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