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Construction 11.1 :

To construct the bisector of a given angle.

Given an angle ABC, we want to construct is bisector

Steps of Construction:

  1. Taking B as centre and any radius,  draw an arc to intersect the rays BA and BC,  say at E and D respectively.
  2. 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.
  3. 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


  1. Chapter 11 Class 9 Constructions
  2. Concept wise
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CA Maninder Singh
CA Maninder Singh is a Chartered Accountant for the past 7 years. He provides courses for Practical Accounts, Taxation and Efiling at teachoo.com .