Pappus's theorem

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.