Pappus's theorem

Author:: Zoltán Kovács

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.

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