Question

line l is the bisector of angle A and B is any point on l.BP and BQ are perpendiculars from B to the arms of angle A.show that: 1) triangle APB congruent to the triangle AQB

Answer 1

In ΔABP and ΔAQB
∠BAP = ∠QAB (line l is the bisector)
∠BPA = ∠BQA (perpendiculars or 90°)
AB = AB (common)
∴ By AAS rule, ΔAPB ≌ ΔAQB.