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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.

 Jan 10, 2020
 #1
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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

 

 

 

cool cool cool

 Jan 10, 2020

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