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  1. Chapter 11 Class 9 Constructions
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To construct a triangle, given its base, a base angle and sum of other two sides. Given the base BC, a base angle ∠B and the sum AB + AC, we need to construct Δ ABC Steps of Construction: Draw base BC and at point B make an angle XBC equal to the given angle. Cut a line segment BD equal to AB + AC from ray BX. Join DC. Draw perpendicular bisector PQ of line DC. Let PQ intersect BD a point A. Join AC. Then, Δ ABC is the required triangle. Justification We need to prove that AB + AC = BD. Given Base BC and ∠B In Δ ACD,   PQ is the perpendicular bisector of CD i.e. AR is the perpendicular bisector of CD ⇒ CR = DR & ∠ ARC = ∠ ARD = 90° Now, in Δ ADR and Δ ACR   AR = AR     ∠ ARC = ∠ ARD   CR = DR ∴ Δ ADR ≅  Δ ACR ⇒ AC = AD Now, BD = AB + AD BD  = AB + AC Thus, our construction is justified

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Davneet Singh
Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He provides courses for Mathematics from Class 9 to 12. You can ask questions here.
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