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 .
To prove: AB||CD
Construction: Draw &
We know that Angle of incidence = angle of reflection. Therefore, and as shown in the figure.
We have because they are perpendicular to two parallel lines.
BC is transversal of BX and YC. Therefore, (Alternate interior angles)
(These are alternate interior angles)
If, alternate interior angles are equal then lines are parallel. Therefore,