Cognitive development refers to the development of mental processes such as thinking, memory, problem-solving, and reasoning. Adolescents begin to think more systematically and logically during this stage, which is a key feature of cognitive development.
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.