Question

Question 6
PQ and RS are two mirrors placed parallel to each other. An incident ray AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes the mirror RS at C and again reflects back along CD. Prove that AB||CD

Answer 1

Let us draw $BM\perp PQ$ and $CN\perp RS$.
$AsPQ||RS$,
$BM||CN$.
Thus, BM and CN are two parallel lines and a transversal line BC cuts them at B and C respectively.
$\therefore \angle 2=\angle 3$ (Alternate interior angles)
However, $\angle 1=\angle 2and\angle 3=\angle 4$ (By laws of reflection)
$\therefore \angle 1=\angle 2=\angle 3=\angle 4$
Also, $\angle 1+\angle 2=\angle 3+\angle 4$
$\angle ABC=\angle DCB$
However, these are alternate interior angles.
$\Rightarrow AB||CD$