It’s been a long time since my last post, mainly due to my laziness. Hopefully I can gradually gain some momentum back.
Anyway, here is a proof that all triangles are equilateral (all sides are equal). He first proved that any two arbitrary sides have the same length (using congruent triangles), and so the triangle must be equilateral.
Actually, it took me a while to figure out what goes wrong. I would suggest drawing a triangle (preferably with extreme side ratios) on the paper yourself to find the fault.