In the given figure, m and n are two plane mirrors perpendicular to each other. Show that the incident ray CA is parallel to the reflected to the ray BD.
Answers
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
o
⇒90
o
+∠2+∠3=180
o
⇒∠2+∠3=90
o
⇒2(∠2+∠3)=180
o
(Multiplying both sides by 2)
⇒2(∠2)+2(∠3)=180
o
⇒∠CAB+∠ABD=180
o
(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)
Answer:
Step-by-step explanation:
Since Angle of incident = Angle of reflection
Ang 1 = Ang 2
Similarly,
Ang 3 = Ang 4
In triangle APB
Ang P + Ang 1 + Ang 2 = 180
90 + 1 + 2 = 180
1+2 = 180-90
1+2 = 90
therefore AB II CD