Newton line
In Euclidean geometry the Newton line is the line that connects the midpoints of the two diagonals in a convex quadrilateral other than a parallelogram.
Properties
The line segments and that connect the midpoints of opposite sides of a convex quadrilateral intersect in a point that lies on the Newton line. This point bisects the line segment that connects the diagonal midpoints.By Anne's theorem and its converse, any interior point P on the Newton line of a quadrilateral has the property that
where denotes the area of triangle.
If the quadrilateral is a tangential quadrilateral, then its incenter also lies on this line.