Question

Class:-9th (CBSE) (lesson no.6:- lines and angles)✨✨✨✨
Question:- In the given figure, m and n are two points plane mirror perpendicular to each other.Show that incident rays CA is parallel to reflected ray BD.
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Answer 1

Step-by-step explanation:

Given: Two plane mirrors m and n, perpendicular to each other. CA is incident ray and BD is reflected ray.

To Prove: CA∥DB

Construction: OA and OB are perpendiculars to m and n respectively.

Proof:

∵m⊥n,OA⊥m and OB⊥n

∴∠AOB=90

o

(Lines perpendicular to two perpendicular lines are also perpendicular.)

In ΔAOB,

∠AOB+∠OAB+∠OBA=180 degree

⇒90 degree

+∠2+∠3=180 degree

⇒∠2+∠3=90 degree

⇒2(∠2+∠3)=180 degree

(Multiplying both sides by 2)

⇒2(∠2)+2(∠3)=180 degree

⇒∠CAB+∠ABD=180 degree

(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)