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).
CT h*sqrt(2) h CB
 =  =  = 
CA 2*h h*sqrt(2) CT
Therefore, triangles ACT and TCB are similar.
Therefore, angles CAT and CTB are equal.
Angle z is an exterior angle of triangle CBT.
Therefore, angle(z) = angle(CBT) + angle(CTB)
= angle(CBT) + angle(CAT)
= angle(y) + angle(x)

Posted by Bractals
on 20051224 04:35:23 