Desargues

Desargues' theorem is a fundamental idea in projective geometry that describes a special relationship between two triangles. It states that if one triangle's corresponding lines all meet at a single point (called the perspective point), then the points where their corresponding sides intersect will all lie on a single straight line (called the perspective line). Conversely, if the sides of two triangles intersect along a straight line, then the lines connecting their corresponding vertices meet at a single point. This theorem reveals deep connections between perspective and alignment, illustrating how geometric figures relate through projection and perspective.