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).

angle z = 45 degrees because triangle CDT is isosceles (DT=CD=h). 

So now all we have to prove is (angle x) + (angle y) = 45 degrees.

Posted by MindRod on 2005-12-23 22:24:58