Q. 224.3( 23 Votes )

Prove that any tw

Answer :

Given: ΔABC in which AD is a median.


To prove: AB+AC>2AD


Construction: Produce AD to E such that AD = DE. Join EC.



Proof:


In Δ ADB and ΔEDC,


AD = DE (By construction)


BD = DC ( D is midpoint of BC)


ADB = EDC (Ver. Opp. Angles)


By SAS congruency,


Δ ADB ΔEDC


AB = EC (By CPCT)


In ΔAEC,


As sum of two sides is greater than third side.


AC + EC > AE


AD = DE


AE = AD + DE and EC = AB


AC + AB > 2 AD


Hence proved


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