Question

please answer this as quick as possible

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]