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In the adjacent figure. P and Q are points on lines, OA and OB,respectively, of the LAOB, such that OP 00 A set square used toistrict perpendiculars to OA and OB at P and O respectively. ThePerpendicalars meet at C Prove that OC is the angle bisector of AOB |
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Answer» Given, OP = OQ angle(OPC) = angle(OQC) = 90° In ΔOPC and ΔOQC OP = OQ angle(OPC) = angle(OQC)OC = OCtherfore, By SAS rule,ΔOPC and ΔOQC are congruent. => angle(POC) = angle(QOC)Therfore,OC is the angle bisector of angle(POQ)hence proved. |
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