Construction 11.1 :
To construct the bisector of a given angle.
Given an angle ABC, we want to construct is bisector
Steps of Construction:
- Taking B as centre and any radius, draw an arc to intersect the rays BA and BC, say at E and D respectively.
- Next, taking D and E as centres and with the radius more than 1/2 DE, draw arcs to intersect each other, say at F.
- Draw the ray BF.
This ray BF is the required bisector of the angle ABC.
We have to prove BF bisects ∠ ABC,
i.e. we have to prove ∠ EBF = ∠ DBF
Join DF and EF.
In Δ BEF and Δ BDF,
BE = BD
EF = DF
BF = BF
∴ ∆BEF ≅ ∆BDF
∴ ∠ EBF = ∠ DBF
Thus, BF is bisector of ∠ ABC