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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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 8 years. He provides courses for Maths and Science at Teachoo. You can check his NCERT Solutions from Class 6 to 12.