Answer :

Let us first draw a figure for above question.


Given:


D is any point on the segment BC


We know one basic fact about triangles that the sum of any two sides of a triangle is always greater than the third side.


So let us first consider Δ ADB


AB + BD > AD …………………….. (i)


Similarly let us consider the Δ ADC


AC + DC >AD …………………….. (ii)


Let us now add the equations (i) and (ii)


AB + AC + BD + DC > AD + AD


From the figure we observe that total length BC = BD + DC


AB + AC + BC > 2 × AD


Hence Proved.


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