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Last updated at Oct. 5, 2018 by Teachoo

Transcript

Construction 11.4 : 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 2. Now, let’s draw ∠ B Construct angle B from point B. Let the ray be BX 3. Open the compass to length AB + AC. From point B as center, cut an arc on ray BX. Let the arc intersect BX at D 4. Join CD Now, we will draw perpendicular bisector of CD Check Construction 11.2, Class 9 on how to draw perpendicular bisector 6. Mark point A where perpendicular bisector intersects BD Join AC ∴ Δ ABC is the required triangle ∴ Δ ABC is the required triangle Now, In Δ ADR and Δ ACR AR = AR ∠ ARD = ∠ ARC DR = CR ∴ Δ ADR ≅ Δ ACR ⇒ AC = AD Now, BD = AB + AD BD = AB + AC Thus, our construction is justified

About the Author

Davneet Singh

Davneet Singh is a graduate from Indian Institute of Technology, Kanpur. He has been teaching from the past 9 years. He provides courses for Maths and Science at Teachoo.