ABE and ADF are equilateral triangles inside and outside
respectively of square ABCD.

Prove that C, E, and F are collinear.

The figure described has 6 equal length segments.
Draw segments CE and EF which are bases of isosceles triangles EBC and EAF.
angle EBC = 90-60 = 30 so angle BEC=75
angle EAF = 90+60-60 = 90 so angle AEF = 45

angle CEF = angles BEC + angle BEA + angle AEF = 75+60+45 = 180

Since the angle is 180 degrees, the points C, E and F are collinear.

Posted by Jer on 2013-10-24 14:19:49