Question

Mid-points of all sides of parallelogram are joined in such a way that a quadrilateral is formed. The formed quadrilateral is

• A. Parallelogram
• B. Trapezium
• C. Kite
• D. Rhombus

Answer 1

The correct option is A Parallelogram


Let $ABCD$ is the parallelogram and $E$, $F$, $G$ and $H$ are the midpoints of sides $AB$, $BC$, $CD$ and $DA$ respectively.
Now, all the points are joined such that $EFGH$ is the quadrilateral.

Draw diagonal $AC$.

Now, In $△ABC$
As $E$ and $F$ are mid points of sides $AB$ and $BC$ respectively so $EF||AC$ (by mid point theorem)

Mid-point theorem: Line joining mid points of two sides of a triangle is parallel to the third side of the triangle.

Similarly, in $△ADC$
$GH||AC$(by mid point theorem)

So, $EF||GH$

Now draw diagonal $BD$

Now, taking $△ABD$
$HE||BD$( by midpoint theorem)
and in $△CBD$
$GF||BD$( by midpoint theorem)

So, $HE||GF$

As, opposite sides are parallel hence the quadrilateral so formed is parallelogram.
Hence, option $\left(a\right)$ correct.