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