If D,E,F are midpoints of sides BC,CA,AB respectively , prove that AD and FE bisect each other
Answers
EF is joined.
F and E are the midpoints of Sides AB and AC respectibely .
Therefore FE=1/2 BC and ||BC
in quadrilateral BDEF FE=1/2BC=BD and||BD
Therefore, BDEF is a parallelogram and DF and BE are its diagonals.
We know that diagonals of a parallelogram bisects each other
therefore BE bisects DF
Similarly, it can be proved that CF bisects DE.
Answer:
It is given that,
D,E,F are mid-points of sides BC,CA and AB of a △ABC
To prove:
AD and FE bisect each other
Construction:
Join ED and FD
Proof:
By mid point theorem,
D and E are the midpoints of BC and AB
⇒DE∥AC⇒DE∥AF ... (1)
D and F are the midpoints of BC and AC
⇒DF∥AB⇒DF∥AE ...(2)
From equation (1) and (2),
ADEF is a parallelogram.
We know that,
The diagonals of a parallelogram bisect each other.
∴AD and FE bisect each other.
Hence, proved.
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