Mathematics
D, E and F are the mid-points of the sides AB, BC and CA of an isosceles △ ABC in which AB = BC. Prove that △ DEF is also isosceles.
Mid-point Theorem
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Answer
Join D, E and F.
Given,
AB = BC = x (let)
Given,
D, E and F are mid-points of sides AB, BC and AC respectively.
By mid-point theorem,
The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it.
∴ DF = , FE = and DE = .
In △ DEF,
DF = FE.
∴ △ DEF is an isosceles triangle.
Hence, proved that DEF is an isosceles triangle.
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