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Question

D,E and F are respectively the mid-points of the sides BC,CA and AB of a ABC
Show that BDEF is a parallelogram.
1369581_995ced7e5798413bb462f2520113919b.PNG

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Solution

In ABC,
F is the mid-point of side AB and
E is the mid-point of side AC
EFBC
In a triangle, the line segment joining the mid-points of any two sides is parallel to the third side.
EFBD ......(1)
In ABC,
D is the mid-point of side BC and
E is the mid-point of side AC
DEAB
In a triangle, the line segment joining the mid-points of any two sides is parallel to the third side.
DEFB ......(2)
Now, FEBD and DEFB from (1) and (2)
In BDEF, both pairs of opposite sides are parallel
BDEF is a parallelogram.

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