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 re: only geometry? by Richard)

"And yes, cutting triangles out of paper and putting them together would be in the spirit of the intended approach, and perhaps "similar trangles" might somehow be found in this way that would lead to a good proof."

Richard explained what happens to the wording of the problem in the queue, and his quite right, but not with the first part of the phrase above.

The intention is to achieve a proof using similarity of triangles, and of course, with the knowledge that the internal angles of a triangle adds to 180 degrees, the external angle is the sum of the two others internal angles, etc...  

Posted by pcbouhid on 2005-12-23 15:09:48