In the adjoining figure AB, EF and CD are parallel lines. Given that GE = 5 cm, GC = 10 cm and DC = 18 cm, then EF is equal to:

In ΔGEF and ΔGCD, we have
∠EFG = ∠GCD (Alternative angle)
∠EFG = ∠CGD (Vertically opposite angles)
ΔGEF ~ ΔGCD
Thus,
$$\eqalign{ & \frac{{{\text{GE}}}}{{{\text{CG}}}} = \frac{{{\text{EF}}}}{{{\text{CD}}}} \cr & {\text{or, }}\frac{5}{{10}} = \frac{{{\text{EF}}}}{{18}} \cr & {\text{or,}}\,{\text{EF}} = 9\,{\text{cm}} \cr} $$