The quadrilateral obtained by joining the mid-points (in order) of the sides of quadrilateral ABCD is :

1. rectangle

2. rhombus

3. parallelogram

4. square

Let ABCD be the quadrilateral. P, Q, R and S are the mid-points of sides AB, BC, CD and DA.

Join PQRS, AC and BD.

By mid-point theorem,

The line segment joining the mid-points of any two sides of a triangle is parallel to the third side and is equal to half of it.

In △ ABC,

P and Q are mid-points of sides AB and BC respectively.

∴ PQ || AC and PQ = $\dfrac{1}{2}AC$ (By mid-point theorem) …….(1)

In △ ADC,

S and R are mid-points of sides AD and DC respectively.

∴ SR || AC and SR = $\dfrac{1}{2}AC$ (By mid-point theorem) ……..(2)

From equations (1) and (2), we get :

⇒ PQ = SR and PQ || SR.

In △ ABD,

P and S are mid-points of sides AB and AD respectively.

∴ SP || BD and SP = $\dfrac{1}{2}BD$ (By mid-point theorem) …….(3)

In △ CBD,

Q and R are mid-points of sides BC and DC respectively.

∴ QR || BD and QR = $\dfrac{1}{2}BD$ (By mid-point theorem) ……..(4)

From equations (3) and (4), we get :

⇒ SP = QR and SP || QR.

Since, opposite sides are parallel and equal.

∴ PQRS is a parallelogram.

Hence, Option 3 is the correct option.