Geometry > Challenging problems
Challenging geometry problem: arbitrary quadrilaterals
- In quadrilateral ABCD, E, F, G and H are midpoints of sides AB, BC, CD and
DA respectively.
Prove that quadrilateral EFGH is a parallelogram.

- In quadrilateral ABCD, E and F are midpoints of sides AD and BC
respectively, G and H are midpoints of diagonals BD and AC respectively.
Prove that EF and GH bisect each other.
