Formulate Theorems in Multiple Ways: Pappus's Hexagon Theorem

RandomInstance and FindGeometricConjectures can be used to discover complex geometric theorems, while allowing flexibility in how the scene is described.

Pappus's hexagon theorem states that for a crossed hexagon where every other vertex is collinear, the points of intersection of the three pairs of opposite sides are collinear. Represent the hypotheses of Pappus's hexagon theorem as a GeometricScene.

Successfully conjecture the conclusion.

Use different but equivalent hypotheses to generate yet another instance of the same abstract scene.

Again, successfully conjecture the conclusion.