prove that AB + BC+ CA > 2AD
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Step-by-step explanation:
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Step-by-step explanation:
Given:- In △ABC, AD is median of triangle, on the side BC.
To Prove:- AB + BC + AC > 2AD
Proof:-
In △ABD,
AB + BD > AD (Sum of two sides of a triangle is greater than the third side) ----- 1
Similarly, In △ACD,
AC + CD > AD (Sum of two sides of triangle is greater than the third side) ----- 2
Thus, adding eq.1 and eq.2, we get,
AB + BD + AC + CD > AD + AD
AB + (BD + CD) + AC > 2AD [Associative Property]
Thus,
AB + BC + AC > 2AD
Hence, proved
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