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Question
Let Abc Be an Isosceles Triangle in Which Ab = Ac. If D, E, F Be the Mid-points of the Sides Bc, Ca and a B Respectively, Show that the Segment Ad and Ef Bisect Each Other at Right Angles.
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Solution
Since D, E and F are the midpoints of sides
BC, CA and AB respectively
∴ AB || DF and AC || FD
AB || DF and AC || FD
ABDF is a parallelogram
AF = DE and AE = DF
`1/2`AB = DE and `1/2` AC = DF
DE = DF ( ∵ AB = AC )
AE = AF = DE = DF
ABDF is a rhombus
⇒ AD and FE bisect each other at right angle.
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