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Construction 11.1 :
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To construct the bisector of a given angle.

Given an angle ABC, we want to construct is bisector

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Steps of Construction:
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- 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.

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Justification
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We have to
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prove BF bisects ∠ ABC,
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i.e. we have to prove
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∠
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EBF = ∠ DBF
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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