Line l is the bis

Given: l is the bisector of an ∠A, BP and BQ are perpendiculars

(i)
To Prove: 
Proof:
In

∠P = ∠Q (Right angles)

∠BAP = ∠BAQ (l is the bisector)

AB = AB (Common)

Congruent Triangles - Two angles and an opposite side (AAS) Definition: Triangles are congruent if two pairs of corresponding angles and a pair of opposite sides are equal in both triangles.

Therefore,

By AAS congruence,

Hence, Proved.

(ii) BP = BQ (By c.p.c.t)

Therefore,

B is equidistant from the arms of ∠A