m and n are plane mirrors perpendicular to each other. Prove that incident ray CA (to mirror n ) is parallel to reflected ray (to mirror m ) BD. 

Respected Sirs,

Please answer my this question as soon as possible. I tried to insert the figure from ms-paint file but was unable to do so. But I believe that the question is self descriptive.

Let us draw BM ⊥ PQ and CN ⊥ RS.

As PQ || RS,

Therefore, BM || CN

Thus, BM and CN are two parallel lines and a transversal line BC cuts them at B and C respectively.

∴∠2 = ∠3 (Alternate interior angles)

However, ∠1 = ∠2 and ∠3 = ∠4 (By laws of reflection)

∴ ∠1 = ∠2 = ∠3 = ∠4

Also, ∠1 + ∠2 = ∠3 + ∠4

∠ABC = ∠DCB

However, these are alternate interior angles.

∴ AB || CD