1.

How to prove that sum of two sides of a triangle is greater than twice the median?

Answer»

Let D be the midpoint of BC,
⇒AD is a median of ΔABC
Now we need to prove AB+AC>2AD
extend AD to E such that AD=DE
⇒AE=2AD,
Draw lines BEandEC, as SHOWN in the figure.
⇒ABEC is a parallelogram.
⇒BE=AC.
Consider ΔABE
Recall that the sum of any two sides of a triangle is greater than the length of the third side,
⇒AB+BE>AE
⇒AB+AC>2AD ....... (proved)


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