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Question
D, E and F are the mid-points of the sides AB, BC and CA of an isosceles ΔABC in which AB = BC. Prove that ΔDEF is also isosceles.
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Solution
E and F are mid-points of BC and AC
Therefore, EF = `(1)/(2)"AB"`......(i)
D and F are mid-points of AB and AC
Therefore, DF = `(1)/(2)"BC"`......(ii)
But AB = BC
From (i) and (ii)
EF = DF
Therefore, ΔDEF is an isosceles triangle.
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