Question

AD is median of triangleABC . Prove thay;AB +AC>2AD

Answer 1

Given: AD is a median of the triangle ABC.Required to prove: AB+AC>2AD.Construction: AD is extended to G such that AD=DG. B,G and C,G are joined. Proof: In triangles ABD and DGC, 1. AD=DG [construction]. 2. BD=DC [since AD is a median (given)] 3. included angle ADB= included angle CDG. Therefore, triangles ABD and DGC are congruent. [SAS congruency] AB = CG, since they are corresponding sides of congruent triangles. In triangle ACG, AC+CG>AG. [sum of two sides of a triangle is greater than the third side.] or, AC+AB>AD+DG. [since AB=CG ( proved earlier)] or, AB+AC>AD+AD [since AD=DG ( by construction)] or, AB+AC> 2AD. [Proved

Answer 2

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