Given a complete quadrilateral ABDEF (see the figure below) M1, M2, and M3 are the midpoints of AC, BD, and EF, respectively. The line segments MAMC and MBMD that connect the midpoints of opposite sides AB with CD and BC with AD intersect at M4. Prove that M1,M2,M3, and M4 are collinear points.
Newton line is the line that connects the midpoints of the two diagonals in a quadrilateral other than a parallelogram.
The midpoints of the diagonals of a complete quadrilateral lie on a line called Newton-Gauss line.
Complete quadrilateral ABCDEF is the figure determined by four lines, no three of which are concurrent, and their six points of intersection A, B, C, D, E, and F.
This step-by-step interactive illustration was created with GeoGebra.
GeoGebra is free and multi-platform dynamic mathematics software for all levels of education that joins geometry, algebra, tables, graphing, statistics and calculus application, intended for teachers and students. Many parts of GeoGebra have been ported to HTML5.
Ten problems: 1411-1420
HTML5 and Dynamic Geometry
View or Post a solution