Dynamic Geometry 1462: Newton-Line, Newton-Gauss Line, Complete Quadrilateral, Midpoints of Sides and Diagonals

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

Newton line is the line that connects the midpoints of the two diagonals in a quadrilateral other than a parallelogram.

Newton-Gauss line

The midpoints of the diagonals of a complete quadrilateral lie on a line called Newton-Gauss line.

Complete quadrilateral

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.

Midpoint

Midpoint of a segment: the point on a line segment dividing it into two segments of equal length.

Static Diagram of Dynamic Geometry 1462: Newton-Gauss Line

Dynamic Geometry 1462: Newton-Line, Newton-Gauss Line, Complete Quadrilateral, Midpoints of Sides and Diagonals, Step-by-step Illustration. Using GeoGebra


Poster of the Newton Line and Newton-Gauss Line using iPad Apps

Poster of Problem 1462, Newton-Line, Newton-Gauss Line, Complete Quadrilateral, Midpoints of Sides and Diagonals, Step-by-step Illustration, GeoGebra, iPad

Classroom Resource:
Interactive step-by-step animation using GeoGebra

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Ten problems: 1411-1420
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