Question

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 Fig. 7.20). Show that:

(i) ∆ APB ≅ ∆ AQB

(ii) BP = BQ or B is equidistant from the arms of ∠A.

Answer 1

In ∆APB and ∆AQB,

∠APB = ∠AQB (Each 90º)

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

AB = AB (Common)

∠∆APB ∠∆AQB (By AAS congruence rule)

∴ BP = BQ (By CPCT)

rms of ∠A. Or, it can be said that B is equidistant from the a