An interesting collinearity

The following interesting result was experimentally discovered in 2018 by my long time mentor and colleague Piet Human (retired from the University of Stellenbosch, now at the Ukuqonda Institute) while he was developing some elementary geometry materials about lines for primary school learners.

Initial Conjecture:
Draw 3 rays from a point J to intersect 2 rays drawn from a point O and label the intersections as shown below. Then the intersection I of the diagonals of quadrilateral ECFB, the intersection H of the diagonals of quadrilateral ADFC are collinear with the point O.

Explore: Drag any of the vertices/points to change the configuration below to explore and verify the conjecture above. Also click on the provided "Show Additional Properties" button. What do you observe?


1) Can you explain why (prove that) the above conjectures are true?
2) Click on this Show Hint button if necessary.

Back to "Dynamic Geometry Sketches"

Back to "Student Explorations"

Michael de Villiers, created 23 February 2019.