Discover the fallacy in the following “proof”: 45 = 60
Proof : Construct an equilateral triangle ABC. On side AB construct an isosceles right triangle ADB with AB as the hypotenuse. Construct EB on BC so that EB ~= BD. Let F be the midpoint of AD and connect E to F with a ray that extended will meet AB in a point G. Construct GD. Now construct the perpendicular bisectors of GD and GE. Because GD and GE are not parallel, the perpendicular bisectors must meet at a point K. Connect K with points G, D, E, and B.
Now, GK ~= KD and GK ~= KE (K lies on the perpendicular bisector of each of the segments GD adn GE), KD ~= KE. By construction DB ~= EB. Therefore angleKBD ~=angleKBE by SSS congruence and KBD ~= KBE. By subtraction DBG ~= EBG. But measure of angle DBG = 45 and measure of angle CBG = 60. Therefore, 45 = 60.