Desargues' theorem | plane geometry | intermediate level

Episode 88.

Desargues' theorem | plane geometry | intermediate level.

Branch of mathematics: plane geometry.
Difficulty level: intermediate.

Desargues' theorem. Let $ABC$ and $A'B'C'$ be triangles. Then the intersection points of the lines containing the corresponding sides of the triangles (the intersection points of the lines $AB$ and $A'B'$, of the lines $BC$ and $B'C'$, of the lines $CA$ and $C'A'$) are collinear or these 3 pairs of lines are all parallel (inside the pairs, but not necessarily between the pairs; so, $AB \parallel A'B'$, $BC \parallel B'C'$, $CA \parallel C'A'$) if and only if the lines connecting the corresponding vertices of the triangles (the lines $AA'$, $BB'$, $CC'$) intersect at a single point or all 3 are parallel to each other.

Notice that, in the video, I forgot the special cases of parallel lines.

Mathematics. Geometry. Plane geometry.
#Mathematics #Geometry #PlaneGeometry

The same video on YouTube:
https://youtu.be/GPNQzkEzd6A

The same video on Telegram:
https://t.me/mathematical_bunker/111