#### Answer

a) BG = 12
b) GE = 2
c) DG = $8\sqrt3$

#### Work Step by Step

a) A theorem states that BG equals 2/3 of BF. Thus:
$BG = 18 \times (2/3) = 12 $
b) GE is half of AG. Thus:
$GE = .5(4) = 2$
c) Using the same method as in b), we know that DG is twice the value of CG. Thus:
$ DG = 2 (4\sqrt{3}) = 8\sqrt3$