Question

What figure is formed by joining the mid points of the pairs of adjacent sides of a quadrilateral?

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

Answer 1

Answer: (D)

Parallelogram

A quadrilateral ABCD, in whcih P, Q, R, S are the mid-points of AB, BC, CD and DA respectively.
To prove : Quadrilateral PQRS is a parallelogram.
Construction : Join A to C.
Proof : In $\Delta$ ABC, P and Q are mid-points of AB and BC respectively.
$\therefore$ PQ || AC and PQ = $\frac{1}{2}$ AC (mid-point theorem)
Again, In $\Delta$DAC, R and S are mid-points of sides CD and AD respectively.
$\therefore$ SR || AC and SR = $\frac{1}{2}AC$(mid-point theorem)
Now, PQ || AC and SR || AC $\to$ PQ || SR
Again, $PQ=\frac{1}{2}AC=SR\Rightarrow PQ=SR$
$\therefore$ PQ || SR and PQ = SR
Hence, PQRS is a parallelogram