Line is the bisector of an and B is any point on . BP and BQ are perpendiculars from B to the arms of (See figure). Show that:
(ii) BP=BQ or B is equidistant from the arms of .
In and , we have
(It is given that AB is the bisector) (1)
(Each equal to ) (3)
Therefore, by AAS congruence rule, we have .
From solution (i), we know that .
Therefore, BP=BQ (Corresponding parts of congruent triangles are equal)