In this paper, we show that a point of division divides a related line segment in the same ratio on the plane with generalized absolute value metric and Euclidean plane. Then the coordinates of the division point can be determined by the same formula as in the Euclidean plane. In the latter parts of the work, we give Ceva's and Menelaus'es theorems and the theorem of directed lines on the plane with generalized absolute value metric.

In this paper, we first give the Pythagorean theorem on the plane with generalized absolute value metric and show that the converse of the Pythagorean theorem is not true in this plane. Secondly, we give necessary and sufficient conditions for a triangle in this plane to have a right angle. Finally, we give a formula for the area of a triangle on this plane.