Editing Midpoint (section)

===Quadrilateral===

*The two [[Quadrilateral#Bimedians|bimedians]] of a [[Convex polygon|convex]] [[quadrilateral]] are the line segments that connect the midpoints of opposite sides, hence each bisecting two sides. The two bimedians and the line segment joining the midpoints of the diagonals are [[Concurrent lines|concurrent]] at (all intersect at)a point called the "vertex centroid", which is the midpoint of all three of these segments.<ref name=Altshiller-Court>Altshiller-Court, Nathan, ''College Geometry'', Dover Publ., 2007.</ref>{{rp|p.125}}

*The four "maltitudes" of a convex quadrilateral are the perpendiculars to a side through the midpoint of the opposite side, hence bisecting the latter side. If the quadrilateral is [[Cyclic quadrilateral|cyclic]] (inscribed in a circle), these maltitudes all meet at a common point called the "anticenter".

*[[Brahmagupta's theorem]] states that if a cyclic quadrilateral is [[Orthodiagonal quadrilateral|orthodiagonal]] (that is, has [[perpendicular]] [[diagonals]]), then the perpendicular to a side from the point of intersection of the diagonals always goes through the midpoint of the opposite side.

*[[Varignon's theorem]] states that the midpoints of the sides of an arbitrary quadrilateral form the vertices of a [[parallelogram]], and if the quadrilateral is not self-intersecting then the area of the parallelogram is half  the area of the quadrilateral.

*The [[Newton line]] is the line that connects the midpoints of the two diagonals in a convex quadrilateral that is not a parallelogram. The line segments connecting the midpoints of opposite sides of a convex quadrilateral intersect in a point that lies on the Newton line.