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  1. Chapter 11 Class 9 Constructions
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Construction 11.2 : To construct the perpendicular bisector of a given line segment. Given a line segment AB, we want to construct its perpendicular bisector. Steps of Construction: Taking A and B as centres and radius more than 1/2 AB, draw arcs on both sides of line segment AB (to intersect each other). Let These arcs intersect each other at P and Q. Join PQ. Let PQ intersect AB at the Point M. Then line PMQ is the required Perpendicular bisector of AB. Justification We have to prove PQ is perpendicular bisector, i.e. AM = BM and PMA = PMB = 90 Join A,B to P and A, B to Q In PAQ and PBQ, AP = BP AQ = BQ PQ = PQ PAQ PBQ So, APM = BPM Now , In PAM and PBM, AP = BP PM = PM APM = BPM PMA PMB So, AM = BM & PMA = PMB Also, PMA + PMB = 180 PMA + PMA = 180 2 PMA = 180 PMA = 90 Thus, BM & PMA = PMB = 90 PQ is the perpendicular bisector of AB

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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.