Look at the drawing below, where AB = BC = CD = DT = h, and TD perpendicular to AD:

                                   
                                   o T
                                   |
                                   | (h) 
                                   |
                                   |
  +----------+----------+----------o 
  A    (h)   B    (h)   C    (h)   D

The line AT makes an angle x with AD; the line BT makes an angle y with BD; the line CT makes an angle z with CD.

Using only geometry, prove that (angle x) + (angle y) = (angle z).

(In reply to Solution by Bractals)

I like your solution, Bractals.  But didn't you have to use the Pythagorean formula to determine that |CT| = h*sqrt(2)?  That's algebra, isn't it?  And using the ratios of the sides of triangles smacks a bit of trigonometry.

I think your solution is a close as we're likely to get to a solution using only "geometry".

Nicely done!

Posted by MindRod on 2005-12-24 12:20:19