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).

Paulo,
I'm not sure what you mean by "using only geometry".  I'm not sure much "geometry" exists without algebra and trigonometry.

For example, the formula for the area of a triangle is algebra.  The Pythagorean formula is algebra.
The fact that the sum of the three angles of a triangle sum up to 180 degrees is trigonometry.

Do you want us to cut triangles out of construction paper, reorganize the pieces, and call it a "proof"?

Posted by MindRod on 2005-12-23 12:51:35