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  1. Chapter 11 Class 9 Constructions
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Construction 11.6 : To construct a triangle, given its perimeter and its two base angles. Given the base angles, B and C and AB + AC + BC, we have to construct ABC. Steps of Construction : Draw a line segment XY equal to AB + AC + BC. Make LXY equal to B and MYX equal to C. Bisect LXY and MYX. Let these bisectors intersect at a point A . Draw perpendicular bisectors of line AX and AY Let PQ intersect XY at B and RS intersect XY at C. Join AB and AC Thus, ABC is a the required triangle Justification To justify, we have to prove AB + BC + AC = XY LXY = B MYX = C In AXQ, PQ is the perpendicular bisector of AX, BX = BA Similarly, we can say CY = CA Now, we know that XY = XQ + BC + CY XY = AB + BC + AC In AXQ Since AX = BA BAX = AXB Now, ABC is the exterior angle of triangle AXQ ABC = BAX + AXB ABC = AXB + AXB ABC = 2 AXB ABC = LXY Thus, B = LXY Similarly, we can prove A = MYX Hence justified

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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.