If D,E and F are mid points of the sides AB,BC and CA respectively of an isoceles triangle ABC, prove thatDEF is also isoceles.
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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
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
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