TO CONSTRUCT THE BISECTOR OF A GIVEN ANGLE

Let ABC be the given angle to be bisected.

STEPS :

(i) With B as centre and a suitable radius, draw an arc which cuts ray BA at point D and ray BC at point E.

(ii) Taking D and E as centres and with equal radii draw arcs which intersect each other at point F. In this step, each equal radius must be more than half the length DE.

(iii) Join B and F and produce to get the ray BF.

Ray BF is the required bisector of the given angle ABC.

    Proof : Join DF and EF.

In Δ BDF and Δ BEF :

BD = BE            [Radii of the same arc]

DF = EF            [Radii of the equal arcs]

BF = BF            [Common]

ΔBDFΔBEF        [By SSS]

∠DBF = ∠EBF        [By cpctc]

i.e.,    ∠ABF = ∠CBF

BF bisects ∠ABC.           

Hence Proved.