AD is the median of triangle ABC. is it true that AB+AC+BC2AD? give reasons for your answers.

In triangle ABD,

AB+BD >AD (Sum of two sides of a triangle is greater than the third side) ... (1)

In triangle ACD,

AC+CD>AD (Sum of two sides of a triangle is greater than the third side)  ...(2)

Adding eq. (1) and (2)

AB+(BD+CD)+AC> AD+AD

AB+BC+AC> 2AD

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Yes it is true.

In triangle ABD

AB+BDAD (Sum of two sides of a triangle is greater than the third side) ... (1)

In triangle ACD

AC+CDAD (Sum of two sides of a triangle is greater than the third side) ...(2)

Adding eq. 1 and 2

AB+BD+CD+ACAD+AD

AB+BC+AC2AD

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