Question

If the midpoints of adjacent sides of a quadrilateral are joined, we will get a

• A. Square
• B. rhombus
• C. Parallelogram
• D. trapezium

Answer 1

The correct option is C

Parallelogram

If the midpoints of adjacent sides of a quadrilateral are joined, we will get a parallelogram.
Proof -
Construction - Join $AC$
In $\Delta ABC$, P and Q are the mid-points of $AB$ and $BC$ respectively.
By mid-point theorem, $PQ$$\parallel$$AC$.
Also PQ = $\frac{1}{2}$ AC------------(1)
Similarly, $SR$$\parallel$$AC$.
$\Rightarrow$ $PQ$$\parallel$ $SR$.
Also SR = $\frac{1}{2}$AC-----------------(2)
From (1) and (2) PQ = SR
Similarly, by joining BD, and considering $\Delta BCDand\Delta BAD$, we can prove that $QR$$\parallel$$PS$ and QR = PS
Since opposite sides are equal and parallel , it is a parallelogram.
Hence, $PQRS$ is a parallelogram.