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 || CD.
NCERT Class 9 Mathematics Chapter 6
Page No. 104
Exercise 6.2
Question No. 6
Draw BE⊥PQ and CF⊥RS.
∠1 = ∠2 …(i)[∵ Angle of incident = Angle of reflection]
Similarly,
∠3 = ∠4 …(ii)
and,
∠2 = ∠3 …(iii)[∵ Alternate Angles]
⇒ ∠1 = ∠4 [From the equations (i), (ii) and (iii)]
⇒ 2∠1 = 2∠4
⇒ ∠1 + ∠1 = ∠4 + ∠4
⇒ ∠1 + ∠2 = ∠3 + ∠4 [From the equation (i) and (ii)]
⇒ ∠BCD = ∠ABC
Since, the alternate angles are equal. Hence, AB||CD.