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