Question

if p (1,2) Q(1,0 R(0,1) are the mid points of the sides Ab bc and ca respectively of a triangle Abc find the cordinates of the vertices A,B,C and hence find the are of a triangle ABC

Answer 1

iven: 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

Answer 2

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