Question

D, E and F are respectively the mid-points of the sides BC, CA and AB of a ABC. Show that

• A. BDEF is a parallelogram
• B. Area of DEF = ${}^1{/}_4$ area of ABC
• C. Area of BDEF = ${}^1{/}_2$ of area of ABC
• D. None of these

Answer 1

The correct option is A BDEF is a parallelogram

Given :

$△ABC$ where D, E, F are mid-points of BC, AC and AB respectively.

To prove : BDEF is a parallelogram.

Proof :

In $△ABC$,

F is mid-point of AB,

E is mid-point of AC

Line segments joining the mid-points of two sides of a triangle is parallel to the third side.

Therefore, $FE\parallel BC$

$FE\parallel BD$ ( Parts of parallel lines are parallel )

D is the mid-point of BC and E is the mid-point of AC.

Therefore, $DE\parallel AB$

$DE\parallel FB$

Now, $FE\parallel BD$ and $DE\parallel FB$

In BDEF, both pairs of opposite sides are parallel.

Therefore, BDEF is a parallelogram.