Question

Ad is the median of triangle abc.is it true that ab=bc=ca>2ad?give reasons

Answer 1

Given

A triangle ABC ,

where AD is median of BC



To prove. :- AB+BC+CA>2AD



PROOF :


In triangle ABD,



AB+BD>AD ( Because sum of two sides of a triangle is always greater the third side ) --- (i)


In triangle ADC,



AC+CD>AD ( Because sum of two sides of a triangle is always greater than the third side ) --- (ii)




Now adding (i) and (ii) , we get :



AB + AC + ( BD + CD ) > 2AD



We know that BC and CD are parts of same side.



So, BC + CD = BD



Substituting it in the inequality:



AB + AC + BD > 2AD



[ Hence proved ]

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Answer 2

Given

A triangle ABC ,

where AD is median of BC

To prove. :- AB+BC+CA>2AD

PROOF :

In triangle ABD,

AB+BD>AD ( Because sum of two sides of a triangle is always greater the third side ) --- (i)

In triangle ADC,

AC+CD>AD ( Because sum of two sides of a triangle is always greater than the third side ) --- (ii)

Now adding (i) and (ii) , we get :

AB + AC + ( BD + CD ) > 2AD

We know that BC and CD are parts of same side.

So, BC + CD = BD

Substituting it in the inequality:

AB + AC + BD > 2AD

[ Hence proved ]