I like this as a proof better than the OP. Not only does it avoid the sin2(a)/cos2(a)=1 pitfall but shows clearly the math without use of trig. This part is the yummy bit: >Since a<b and a+b=90 degrees then a<45 degrees, and therefore 'BAD' < 90 degrees, which means that if we draw a line 'l' that is perpendicular to 'BA' at 'B', 'l' would never be parallel with the line 'AD' and they cut each other at a point 'E' like the Figure B.