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.

Guest Jan 10, 2020

#1**+1 **

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

CPhill Jan 10, 2020