Theorem of Desargues

Desargues' Theorem states that if two triangles are positioned so that the lines connecting their corresponding vertices all meet at a single point (are "concurrent"), then the intersections of their corresponding sides will align on a single straight line (are "collinear"). Conversely, if the intersections of corresponding sides are collinear, then the lines connecting the vertices are concurrent. This relationship highlights a deep connection between the angles and intersection points of triangles, forming a foundational principle in projective geometry that relates perspective and alignment.