1. Chapter 11 Class 9 Constructions
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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: 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

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