Question

given line l bisect angle A ....

Answer 1

In triangles AQB and APB ,

Angle QAB = Angle BAP ( the line l bisects angle QAP)

Angle APB = Angle QBA (BP and BQ are perpendicular to AP and BP respectively)

AND AB is common line.
Therefore ,BY Angle Angle Side Congurancy ,
triangle AQB =~ tiangle APB

BY Complementary parts of congurant triangle ,
PB=BQ