Prove that the sum of two sides of a triangle is greater than twice its median.
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∆ ABC and BO is a median and AO = OC
By construction we extend C to B` so that AB || B`C extend BO to B` so , BO = OB` and AB = B`C or AB` = BC
BB` = 2 BO ....{ BO = OB` }
............{ equation 01 }
Statement 1 : The sum of two sides of triangle is always greater then third one.
So, in give triangle
AB + AB` > BB`
AB` = BC .........{by construction}
AB + BC > BB`
AB + BC > 2BO
{BO is a median and by equation 1 we put the value of BB`}
True statement : The sum of two triangle is always greater than the twice of the median of a triangle.
Hence ,
Hence Proved
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