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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