line l is the bisector of an angle ∠ A and B is any point on l. BP and BQ are perpendiculars from B to the arms of ∠ A (see Figure). Show that: (i) Δ APB ≅ Δ AQB (ii) BP = BQ or B is equidistant from the arms of ∠ A.

(i) In ΔAPB and ΔAQB,
∠APB = ∠AQB [∵ Each 90°]
∠PAB = ∠QAB [∵ Line l bisects angle A]
AB = AB [∵ Common]
Hance, ΔAPB ≅ ΔAQB [∵ ASA Congruency Rule]

(ii) BP = BQ [∵ Corresponding parts of congruent Triangles are equal ]