Desargues' Theorem

4.3 - 4.4 Investigate Desargues' Theorem and Its Dual
I hear and I forget;
I see and I remember;
I do and I understand.
—Ancient Proverb

Axiom 5. (Desargues' Theorem) If two triangles are perspective from a point, then they are perspective from a line.

Dual of Desargues' Theorem. If two triangles are perspective from a line, then they are perspective from a point.

Drag the points of the two triangles ABC and A'B'C'.
Drag the center O and the points determining the line a, b, and c.

Dual of Desargues' Theorem

Drag the points l₁ or l₂ of the line to change the axis I.
Drag the points X, Y, Z, A, A', C, or C' to change the triangles.

Timothy Peil, 5 February 2013, Created with GeoGebra