Question

If d and e are mid points of ab and ac and de//bc proof

Answer 1

Given: D,E,F are the mid points of AB,BC,CA

To Prove: DE = EF

Proof: AB = AC (isosceles triangle) 

         ∠B = ∠C (angle opp to equal sides)

         ¹/₂ AB = ¹/₂ AC

         so,DB = CF

         In ΔADF and ΔCEF

             DB = CF (proved above)

             BE = CE (E is the mid point of BC)

            ∠B = ∠C (proved above)

         ∴ ΔADF = ΔCEF (SAS)

              DE = FE (CPCT)

Hence, Proved