Q68 of 93 Page 6

In figure, m and n are two plane mirrors parallel to each other. Show that the incident ray CA is parallel to the reflected ray BD.

    
Given: m and n are parallel to each other.To prove: ray BD || ray CA.Proof:BQ is the normal to the reflecting surface. ⇒ BQ ⊥ n.Similarly, AP is the normal to the reflecting surface.⇒ AP⊥ m.⇒ Since m || n.AP || BQ.  ⇒ ∠QBA = ∠BAP (Alternate angles are equal)∴ 2∠QBA = 2∠BAP     ∠DBA = ∠BAC (The angle of incidence = The angle of reflection)ray BD || ray CA ( Alternate angles are equal ).

More from this chapter

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66 Prove that through a given point we can draw only one perpendicular to a given line. 67 Prove that two lines that are respectively perpendicular to two intersecting lines intersect each other. 69 (v) If two parallel lines are intersected by a transversal, then the interior angles on the same side of the transversal are equal.   70 Fill in blanks in each of the following to make the statement true:
(i) If two parallel lines are intersected by a transversal, then each pair of corresponding angles are …………..
(ii) If two parallel lines are intersected by a transversal, then interior angles on the same side of the transversal are ……………
(iii) Two lines perpendicular to the same line are ………….. to each other.
(iv) If a transversal intersects a pair of lines in such a way that a pair of alternate angles are equal, then the lines are ………….
(v) Two lines parallel to the same line are ……………to each other.
(vi) If a transversal intersects a pair of lines in such a way that the sum of interior angles on the same side of the transversal is 180°,
then the lines are ………….