The following applet illustrates one conditional statement of Desargues's Theorem.
Study the dynamics of this applet carefully. How would you describe what you see?
Try putting it into words.

Wikipedia also provides a detailed description of this fascinating theorem.
This applet illustrates one conditional statement from this theorem (which is actually a biconditional.)
This applet shows that if two trianglesare in perspective centrally, then they are in perspective linearly.The yellow point you see initially see is called the center of perspectivity. The line that contains the resulting purple segment you see is called the axis of perspectivity.