MathDB

6

Part of 1999 Israel Grosman Mathematical Olympiad

Problems(1)

6 midpoints are coplanar, given 3 parallelograms in space

Source: Israel Grosman Memorial Mathematical Olympiad 1999 p6

2/15/2020
Let A,B,C,D,E,FA,B,C,D,E,F be points in space such that the quadrilaterals ABDE,BCEF,CDFAABDE,BCEF, CDFA are parallelograms. Prove that the six midpoints of the sides AB,BC,CD,DE,EF,FAAB,BC,CD,DE,EF,FA are coplanar
geometryparallelogram3D geometrycoplanarmidpoints