Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to? The effect of such a production being made over something so simple is to make people doubt their own intuition. Calling into question the obvious by insisting that it be 'rigorously proved' ... is to say to a student 'Your feelings and ideas are suspect. You need to think and speak our way.
Paul  Lockhart, A Mathematician's Lament: How School Cheats Us Out of Our Most Fascinating and Imaginative Art Form
geometry, intuition, math, mathematics