Question

PQ and rs are two mirrors placed parallel to each other and incident ray ab sticks the mirror PQ at be the reflected ray move along the path BC and strike the mirror address at sea and again reflect back along CD prove that ab parallel to CD

Answer 1

Draw BL⊥PQ and CM⊥RS. As PQ∥RS, so, BL∥CM.

The alternate interior angles are equal, so,

∠LBC=∠MCB (1)

It is known that the angle of reflection is equal to the angle of incidence, therefore,

∠ABL=∠LBC (2)

And,

∠MCB=∠MCD (3)

From equation (1), (2) and (3),

∠ABL=∠MCD (4)

Add equation (1) and (4),

∠LBC+∠ABL=∠MCB+∠MCD

∠ABC=∠BCD

Since, these are the interior angles and are equal, hence, AB∥CD.