Two plane mirrors m and n are placed perpendicular to each other, as shown in figure. An incident ray AB to the first mirror is first reflected in the direction of BC and then reflected by the second mirror in the direction of CD. Prove that AB || CD.

Let BM and CN be the normals to mirrors m and n, respectively and BM and CN intersect at O.

Now, BM⊥m,CN⊥n and m⊥n

But∠ABC and∠BCD are consecutive interior angles formed when the transversal BC cuts AB and CD