5.  Line \small l is the bisector of an angle \small \angle A and B is any point on \small l. \small BP and \small BQ  are perpendiculars from \small B to the arms of \small \angle A (see Fig.). Show that:

  (i) \small \Delta APB\cong \Delta AQB

                                    

Answers (1)

In the given figure consider \small \Delta APB   and   \small \Delta AQB,

(i)      \angle P\ =\ \angle Q                      (Right angle)

(ii)      \angle BAP\ =\ \angle BAQ       (Since it is given that I is bisector)

(iii)     Side AB is common in both the triangle.

Thus AAS congruence, we can write :

                                                     \small \Delta APB\cong \Delta AQB

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