Two mirrors m and n are perpendicular to each other at O .Ray AB is incident to the mirror m at point B and reflected back in the direction BC which is again incident o the mirror n at point C Ray CD is the finally reflected ray.Prove that ray AB is parallel to Ray CD




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So we have theta asthe angle of incidence on the first mirror m.  Let Fie be the angle of incidence on the second mirror  n.

see the enclosed document.

You should remember incident ray = reflected ray. if you see alternate angles are equal then the lines will be parallel. or if corresponding angles are equal then lines are parallel as well 
i may not understand properly. post an image if you can so i can answer better
incident ray is NOT = reflected ray
i mean they are always equal. Search laws of reflection in google