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In Figure, P Q\ a n d\ R S are two mirro...

In Figure, `P Q\ a n d\ R S` are two mirrors placed parallel to each other. An incident ray `A B` strikes the mirror `P Q` at `B ,` the reflected ray moves along the path `B C` and strikes the mirror `R S` and `C` and again reflects back along `C D`. Prove that `A B||C D`.

Text Solution

Verified by Experts

Draw `BEbotPQand CFbotRS`
`rarr BE||CF" "` (`:. Bot s` of parallel lines ar also paallel)
and `anglex=angleb" ".....(1)`
( `:.` angle of incidence -angle of reflection)
Now, `angleb=anglex` (alternate interior angles)
`rArr 2angle2=2anglex`
`rArr angleb+angleb=anglex+anglex`
`rArr anglea+angleb=anglexangley`
`rArr angleABC=angleDCB " "` [from (1) and (2)]
`rArr AB||CD` (`:.` alternate interior angles axiom)
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