Mathematics
If D, E and F are mid-points of the sides AB, BC and CA respectively of an isosceles triangle, ABC, prove that △DEF is also isosceles.
Mid-point Theorem
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Answer
It is given that,
ABC is an isosceles triangle. Let AB = AC = x.
D, E and F are mid-points of the sides AB, BC and CA respectively.
Join D, E and F.
D and E are midpoints of AB and BC
∴ DE || AC and DE = AC = . (By midpoint theorem) ……(i)
F and E are midpoints of AC and BC
∴ FE || AB and FE = AB = . (By midpoint theorem) ……(ii)
From (i) and (ii) we get, DE = FE.
Hence, proved that △DEF is an isosceles triangle.
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