A typical fire suppression team consists of 4 members. These members are trained to carry out various functions, such as fire fighting, emergency medical response, and rescue operations, ensuring the safety of individuals and property.
In the adjoining figure, $\triangle CAB$ is a right triangle, right angled at A and $AD \perp BC$. Prove that $\triangle ADB \sim \triangle CDA$. Further, if $BC = 10$ cm and $CD = 2$ cm, find the length of AD.