# In Fig. 6.33, PQ

Given: Two mirrors are parallel to each other, PQ||RS
To Prove: AB || CD
Proof: Take two perpendiculars BE and CF, As the mirrors are parallel to each other their perpendiculars will also be parallel thus BE || CF

According to laws of reflection, we know that:

Angle of incidence = Angle of reflection

1 = 2 and,

3 = 4 (i)

And,

2 = 3 (Alternate interior angles, since BE, is parallel to CF and a trasversal line BC cuts them at B and C respectively) (ii)
We need to prove that  ∠ABC = ∠DCB
∠ABC = ∠1 +  ∠2 and  ∠DCB =  ∠3 + ∠4

From (i) and (ii), we get

1 + 2 = 3 + 4

⇒ ∠ABC = DCB

⇒ AB parallel CD (Alternate interior angles)
Hence, Proved.

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