**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.

__Justification__

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