Question

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 || CD.​

Answer 1

Given :-

➨ PQ Parallel to RS

➨ AB , BC , CD are the rays

To prove :-

AB Parallel to CD

Construction :-

➨ BM perpendicular to PQ ,

➨ CN perpendicular to RS

Proff :-

Here ,

➨ PQ Parallel to RS [ Given ]

➨BM is parrallel to CN [ Perpendiculars on parrallel are also parrallel ]

★ By law of reflection which states that ,

➨ incident ray = reflected ray

so

➨ Angle 1 = Angle 2

➨ Angle 3 = Angle 4

Now ,

➨ Angle 2 = Angle 3 [ Alternate interior angles ]

➨ If angle 2 = angle 3 then their doubles will also be equal

So

➨ Angle 1 + Angle 2 = Angle 3 + Angle 4

$➨\: \: \sf\bold{\red{Angle \: ABC = Angle \: BCD \: \: }}$

BUT ,

This is pair of alternate interior angles and when alternate interior angles are equal then lines are parallel

So

$➨\: \: \sf\bold{\red{ AB ∥ \: CD \: \: }}$

Therefore Proved

Note :-

★ Figure in attachment