In quadrilateral PLAN opposite sides are equal in length i.e, PL = AN = 6 cm and PN = LA = 5cm. Let’s draw three types of quadrilateral PLAN, let’s see when it will be a rectangle.

Given: A quadrilateral PLAN with

PL = AN = 6 cm

PN = LA = 5 cm

To Do: Draw three types of quadrilateral PLAN, and then assess the criteria as to when it will be rectangle.

Process:

Let us understand what a quadrilateral is.

A quadrilateral is a polygon with four edges and four vertices or corners. There are basic 6 types of quadrilaterals:

- Rectangle

- Square

- Parallelogram

- Rhombus

- Trapezium

- Kite

Let’s draw a type of quadrilateral: Square

A square is a regular quadrilateral, which means that it has four equal sides and four equal angles.

Here, PL = LA = AN = NP = 5 cm

∠PLA = ∠LAN = ∠ANP = ∠NPL = 90°

⇒ PLAN is a square.

Let’s draw another type of quadrilateral: Parallelogram.

A parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

In the quadrilateral PLAN above,

PL ∥ AN and PN ∥ LA

PL = AN and PN = LA

Also, ∠PNA = ∠PLA and ∠LAN = ∠LPN

⇒ PLAN is a parallelogram.

Let’s draw third type of quadrilateral: Rectangle.

A rectangle is a quadrilateral with four right angles. It can also be defined as an equiangular quadrilateral, since equiangular means that all of its angles are equal.

Here, PL = AN = 6 cm and LA = NP = 5 cm

∠PLA = ∠LAN = ∠ANP = ∠NPL = 90°

Hence, PLAN is a rectangle.

So, the criteria required for a quadrilateral to become a rectangle are,

- Opposite sides are parallel and equal

- All angles are right angle