Q. 224.3( 23 Votes )
Prove that any tw
Given: ΔABC in which AD is a median.
To prove: AB+AC>2AD
Construction: Produce AD to E such that AD = DE. Join EC.
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)
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
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