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Question:

In the figure, 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.

Solution:

At surface B, ∠1 = ∠2 (property of reflection)
At surface C, ∠3 = ∠4 (property of reflection)
As the sum of the angles are equal, AB is parallel to CD, ∠2 = ∠3 (Alternate interior angles)
∠1 + ∠2 = ∠3 + ∠4
Alternate interior angles are equal.
∴ AB || CD.