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.

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.

In the figure given below, D and E are mid-points of AB, BC respectively and DF || BC. Prove that DBEF is a parallelogram. Calculate AC if AF = 2.6 cm.

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Prove that four triangles formed by joining in pairs, the mid-points of the sides of a triangle are congruent to each other.

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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

Related Questions

In the figure given below, D and E are mid-points of AB, BC respectively and DF || BC. Prove that DBEF is a parallelogram. Calculate AC if AF = 2.6 cm.

Prove that four triangles formed by joining in pairs, the mid-points of the sides of a triangle are congruent to each other.