Question

Line l is the bisector of an ∠ A and ∠ B is any point on l. BP and BQ are perpendiculars from B to the arms of LA (see figure). Show that (i) ∆APB ≅ ∆AQB (ii) BP = BQ or B is equidistant from the arms ot ∠A.​

Answer 1

Answer:

In △APB and △AQB

∠APB=∠AQB (Each 90

o

)

∠PAB=∠QAB (l is the angle bisector of ∠A)

AB=AB (Common)

∴△APB≅△AQB (By AAS congruence rule)

∴BP=BQ (By CPCT)

It can be said that B is equidistant from the arms of ∠A.