Editing Bisection (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 at a point called the "vertex centroid"  and are all bisected by this point.<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 are [[Concurrent lines|concurrent]] at (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 bisects the opposite side.

The [[perpendicular bisector construction of a quadrilateral|perpendicular bisector construction]] forms a quadrilateral from the perpendicular bisectors of the sides of another quadrilateral.