Question

30. In figure, PQ and RS are two mirrors placed parallel to each other. An incident ray
AB strikes the mirror PQ at B, the reflected ray moves along the path BC and strikes
the mirror RS at C and again reflects back along CD. Prove that AB is parallel to CD.
D



is this correct ​

Answer 1

Explanation:

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Yes it is correct

PQ || RS ⇒ BL || CM

[∵ BL || PQ and CM || RS]

Now, BL || CM and BC is a transversal.

∴ ∠LBC = ∠MCB …(1) [Alternate interior angles]

Since, angle of incidence = Angle of reflection

∠ABL = ∠LBC and ∠MCB = ∠MCD

⇒ ∠ABL = ∠MCD …(2) [By (1)]

Adding (1) and (2), we get

∠LBC + ∠ABL = ∠MCB + ∠MCD

⇒ ∠ABC = ∠BCD

i. e., a pair of alternate interior angles are equal.

∴ AB || CD.