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Question

D, E, and F are, respectively the mid-points of sides BC, CA and AB of an equilateral triangle ABC. Prove that DEF is also an equilateral triangle.

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Solution

Let ABC be the triangle and D, E and F be the mid-point of BC, CA and AB respectively. We have to show triangle formed DEF is an equilateral triangle. We know the line segment joining the mid-points of two sides of a triangle is half of the third side.

Therefore DE=12AB,EF=12BC and FD=12AC

Now, ΔABC is an equilateral triangle

AB=BC=CA

12AB=12BC=12CA

DE=EF=FD

ΔDEF is an equilateral triangle.

1074110_843869_ans_ff2479f702db431bb5ccc531ddc4e944.png

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