Question

In the given figure, I and m are two plane mirrors
parallel to each other. Prove that the incident ray
PQ is parallel to the reflected ray RS.
​

Answer 1

Answer:

Let draw BM ⊥ PQ and CN ⊥ RS.

Given that PQ || RS so that BM || CN

Use the property of Alternate interior angles

∠2 = ∠3 … (1)

∠ABC = ∠1 + ∠2

But ∠1 = ∠2 so that

∠ABC = ∠2 + ∠2

∠ABC = 2∠2

Similarly

∠BCD = ∠3 + ∠4

But ∠3 = ∠4 so that

∠ BCD = ∠3 + ∠3

∠ BCD = 2∠3

From equation first

∠ABC = ∠DCB

These are alternate angles so that AB || CD

Hence proved