D,E,F are respectively th mid-points of the sides AB,BC and CA of ΔABC. Find the ratios of the area of ΔDEF and ΔABC.
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Let DE divide AB and AC then according to midpoint theorem, DE=1/2 BC.
so, DE/BC = 1/2. ......1
Similarly, DF/AC= 1/2 .....2
EF/AB=1/2 .....3
From 1, 2 and 3 we get,
DE/BC = EF/AB = DF/AC.
Thus, triangle DEF ~ triangle ABC.
Area of triangle DEF/area of triangle ABC = 1×1/2×2 = 1/4.
so, DE/BC = 1/2. ......1
Similarly, DF/AC= 1/2 .....2
EF/AB=1/2 .....3
From 1, 2 and 3 we get,
DE/BC = EF/AB = DF/AC.
Thus, triangle DEF ~ triangle ABC.
Area of triangle DEF/area of triangle ABC = 1×1/2×2 = 1/4.
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