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5th Grade Quadrilaterals

Quadrilaterals are known as four sided polygon.

What is a quadrilateral?

A closed figure made of our line segments is called a quadrilateral.

For example:

1.

$Quadrilateral$

The adjoining figure is called a quadrilateral ABCD or BCDA or CDAB or DABC.

2.

$Quadrilateral$

The adjoining figure is called a quadrilateral MNOP or NOPM or OPMN or PMNO.

We already familiar with different quadrilaterals such as square, rectangle, parallelogram, Rhombus, etc. Let us recall them.

Square:

$Square$ Square

A square is a quadrilateral having all its sides equal and all its angles right angle.

AB = BC = CD = AD and

∠A = ∠B = ∠C = ∠D = 90°

Rectangle:

$Rectangle$ Rectangle

A rectangle is a quadrilateral having its opposite sides equal and all its angles right angle.

AB = CD, AD = BC and

∠A = ∠B = ∠C = ∠D = 90°

Parallelogram:

$Problems on parallelogram 1$ Parallelogram

A quadrilateral having its opposite sides and opposite angles equal and opposite sides parallel is a parallelogram.

AB = CD, AD = BC and

∠A = ∠C, ∠B = ∠D

AB and DC are parallel and AD and BC are parallel.

Rhombus:

$Identifying Features of Rhombus$ Rhombus

A quadrilateral with all its sides equal, opposite sides parallel and opposite angles equal

AB = BC = CD = AD,

AB and CD are parallel,

AD and BC are parallel and

∠A = ∠C, ∠B = ∠D

Trapezium:

$Trapezium Diagram$ Trapezium

It is a quadrilateral with its one pair of opposite sides parallel.

AB and CD are parallel.

$Isosceles Trapezium Diagram$ Isosceles Trapezium

When a trapezium has one pair of opposite sides parallel, another pair of opposite sides equal and angles opposite to equal sides equal, it is called isosceles trapezium.

AB and CD are parallel.

AC = BD

∠A = ∠B and ∠C = ∠D

Diagonal of a Quadrilateral:

The line segment that divides a quadrilateral into two triangles, is known as the diagonal.

$Diagonal of a Quadrilateral$

We can observe that AC divides the quadrilateral ABCD into triangles ACD and ABC. Similarly, BD divides the quadrilateral ABCD into triangles ABD and BDC. So, AC and BD are diagonals.

Remember: Any line segment, except its sides, which joins two vertices of a polygon called a diagonal.

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