In trapezoid ABCD, with shorter base CD = 2, leg AD = 6, and anlges CBA and DAB are both 60 degrees. The intersection point of AC and BD is E. F and G are on segments AC and BD, respectively, such that AF = CE and BG = DE. Find the length of FG.
+130511 See the following image :
Let C = (1,0) A = (-4, 3√3) B = (4, 3√3 )
Construct right triangle CHE
And angle ACD = angle BAC
So we can also construct right triangle AIF with AI = CH
And by ASA, right triangles CHE and AIF are congruent
So F has the x coordinate value of -3
And by symmetry, we can note that the x coordinate of G = 3
So FG = 6
