Online Geometry Problems

Online Geometry Problem 828: Quadrilateral, Midpoint, Opposite sides, Diagonals, Concurrent lines, Triangle, Bimedian. Level: High School,  College, Mathematics Education

The figure below shows a quadrilateral ABCD with E,F,G,H midpoints of the sides AB,BC,CD,AD. If M and N are the midpoints of the diagonals AC and BD, prove that (1) EG,FH,MN are concurrent at O, (2) O is the midpoint of EG,FH,MN.
Bimedian is a line segment that joins the midpoints of opposite sides of a quadrilateral like EG and FH.

 

Problem 828: Quadrilateral, Midpoint, Opposite sides, Diagonals, Concurrent lines, Triangle, Bimedian

 

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