Pappus's theorem checked by the Relation Tool

Pappus's hexagon theorem (attributed to Pappus of Alexandria) states that given one set of collinear points , , , and another set of collinear points , , then the intersection points , , of line pairs and , and , and are collinear.
You can check if the theorem is true by dragging the points , , or . You can also drag or as long as you move them on the lines or , respectively. Technically, GeoGebra calculates if the lines and are the same for each change of the construction after you dragged one of the points. Finally, you may use the Relation Tool to confirm your numerical and visual impressions.