Question

Prove that the triangle formed by joining the midpoints of an isosceles triangle is also an isosceles triangle.
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Answer 1

let the isosceles triangle be named as ABC where AB=BC and let D , E and F be the midpoints of sides AB, BC and CA respectively.
now, F and E are midpoints => FE || AB and FE= 1/2 of AB.
similarly, D and F are midpoints => DF || BC and DF=1/2 of BC = 1/2 of AB {Since AB=BC}
therefore, in triangle DEF - EF=DF=1/2 of AB
therefore triangle DEF is also isosceles.

Answer 2

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