Question

In triangle abc ad is perpendicular to bc and point d lies on bc , bd =3cd then prove that

Answer 1

Given: AD is the median of ΔABC.

To prove: AB + AC > 2AD

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

Proof: In ΔABD and ΔCDE

AD = DE      (Construction)

∠ADB = ∠CDE      (Vertically opposite angles)

BD = DC     (AD is the median from A to BC)

∴ ΔABDΔCDE     (SAS congruence criterion) 

⇒ AB = CE         (CPCT)             ...(1)

In ΔACE, 

AC + CE > AE                 (Sum of any two sides of a triangle is greater than the third side)

⇒ AC + AB > AD + DE      [Using (1)]

⇒ AC + AB > AD + AD     (Constriction)

⇒ AC + AB > 2AD

Answer 2

hope it's help u......