In Figure, `m\ and\ n` are two plane mirrors perpendicular to each other. Show that the incident ray `C A` is parallel to the reflected ray `B D`

Explanation

Given: Two plane mirrors m and n, perpendicular to each other. CA is incident ray and BD is reflected ray.To Prove: CA∥DBConstruction: OA and OB are perpendiculars to m and n respectively.
Proof:
∵m⊥n,OA⊥m and OB⊥n
∴∠AOB=90@
(Lines perpendicular to two perpendicular lines are also perpendicular.)
In ΔAOB,
∠AOB+∠OAB+∠OBA=180
⇒90 +∠2+∠3=180@
∠2+∠3=90@
⇒2(∠2+∠3)=180
(Multiplying both sides by 2)
⇒2(∠2)+2(∠3)=180@
⇒∠CAB+∠ABD=180@
(Angle of incidence = Angle of reflection)
∴∠1=∠2 and ∠3=∠4)
⇒CA∥BD (∠CAB & ∠ABD form a pair of consecutive interior angles and are supplementary)