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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Question

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.

KnowledgeBoat · Accepted 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.

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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