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Question
In the given figure, D is mid-point of side AB of ΔABC and BDEC is a parallelogram.
Prove that: Area of ABC = Area of // gm BDEC.
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Solution
Here AD = DB and EC = DB, therefore EC = AD
Again,
∠EFC = ∠AFD .....( Opposite angles )
Since ED and CB are parallel lines and AC cut this line, therefore
∠ECF = ∠FAD
From the above conditions, we have
ΔEFC = ΔAFD
Adding quadrilateral CBDF in both sides, we have
Area of // gm BDEC = Area of ΔABC.
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