Q. 33.9( 23 Votes )
In figure 5.40, ΔABC is an equilateral triangle. Points F,D and E are midpoints of side AB, side BC, side AC respectively. Show that ΔEFD is an equilateral triangle.
Answer :
Given F, D and E are mid-point of AB, BC and AC of the equilateral ΔABC ∴ AB =BC = AC
So by mid-point theorem
Line joining mid-points of two sides of a triangle is 1/2 of the parallel third side.
∴ FE = 1/2 BC =
Similarly, DE = 1/2 AB
And FD = 1/2 AC
But AB =BC = AC
⇒ 1/2 AB = 1/2 BC = 1/2 AC
⇒ DE = FD = FE
Since all the sides are equal ΔDEF is a equilateral triangle.
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