∠EBG=∠FDE-∠FBG=30 =∠E

Then △EGB is an isosceles triangle.

(2) Solution: To make the quadrilateral ACDE a trapezoid with ED as the base, BC⊥DE is needed, and ∠ BFD = 30 can be obtained.

Let the intersection of BC and DE be H.

In a right triangle, DFH, ∠ fdh = 60, DF= DE=2,

Then FH= root number 3.

Then CH=BC-BH=2 root number 3 -(2 root number 3 )=3 root number 3-2.

That is, the height of this trapezoid is 3-2.