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:

Answer: Option D

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