Definition of Quadrilaterals

Based On Topology Quadrilateral Is divided into 3 types

They are:

1. Convex Quadrilateral
2. Concave Quadrilateral
3. Cross Quadrilateral.

Convex Quadrilateral:

This Means four sides of quadrilateral only meet at the vertices two at a time.

This can be shown in diagram as follows..

Concave Quadrilateral:

A Quadrilateral may be concave has an angle exceeding 180 degrees.

This can be shown in diagram as follows..

Cross Quadrilateral:

A Quadrilateral is self intersecting to indicate that pair of non adjacent sides intersect.

This can be shown in diagram format as follows..

1. All Quadrilaterals Have 4 sides.
2. A Square has got 4 equal sides and 4 right angles.
3. A Rhombus has got 4 sides of equal length and opposite sides are parallel and angles are equal.
4. The Rectangle has got 4 right angles and it has got two pairs of equal length sides.
5. A Trazepium has got one pair of parallel sides.
6. A Kite has two pairs of sides next to each other that have equal length.

Now we will see classification of quadrilaterals based on properties..

Property Quadrilateral

Orthogonal Kite, Dart, Rhombus, Square

Having two parallel sides Rectangle, Rhombus, Square, Trapezoid

Having two pairs of parallel sides Rhombus, Square, Rectangle, Parallelogram

Equilateral Rhombus, Square

Equiangular Rectangle, Square

A Quadrilateral which is inscribed in circle is called as a cyclic quadrilateral.

There are different types of quadrilaterals

They are:

1. Parallelogram

2. Square

3. Rectangle

4. Rhombus

5. Trapezoid

A Quadrilateral is said to be parallelogram in which it has two pairs of parallel sides.

Properties of parallelogram:

1. The opposite sides are equal in length

2. The Opposite angles are concurrent.

3. The Diagonals bisect each other.

Formulas for finding area and perimeter for a parallelogram:

Area:

Area of a parallelogram = Base * Height

Perimeter:

Perimeter Of a Parallelogram= 2(a+b)

A Square is a regular quadrilateral and rectangles with equal circumference and the square has a maximum area.

Properties of square:

1. All sides have equal in length
2. All angles are equal to 90 degrees
3. Length Of both diagonals in square are equal
4. The diagonals bisect each other.

Area Of Square = S * S

Perimeter Of Square = 4 * S

Where S=Side length

A Rectangle is a special case of quadrilateral that has four right angles and opposite sides are equal and parallel.

Properties of Parallelogram common to rectangle:

1. Opposite sides of rectangle are equal
2. Opposite angles of rectangle are equal
3. Diagonals of rectangle are divided in their intersection point into two.

The Rectangle has following special properties:

1. The Rectangle is a type of parallelogram having opposite sides are parallel and concurrent.

2. The corner angles are all right angles

3. Diagonals of rectangle are equal and bisect each other.

4. A Square of a diagonal length is equal to sum of squares of its side lengths.

Area Of Rectangle= Length * Breadth

Perimeter Of rectangle = 2(length + Breadth)

A Rhombus is a parallelogram with all four sides having same length and therefore opposite

Angles are equal.

In Rhombus all 4 angles to be same and is just another term for square.

Properties of rhombus:

1. All sides of rhombus are concurrent
2. The Diagonals bisect angles in each corner of rhombus.
3. Diagonals are perpendicular.
4. Opposite angles of a rhombus are equal in measurement.

Rhombus Formulae:

Area Of rhombus= Base * Height (in terms of base and height)

= ½ d1 * d2 ( in terms of diagonals length’s)

Where d1 and d2 are lengths of diagonal 1 and diagonal 2

Perimeter OF Rhombus = 4(a)

a=length of the side.

Trapezoid have 4 sides by definition. Any figure with 4 sides is a Quadrilateral However

Trapezoid has special properties

1. They Have one pair of parallel sides
2. It is a four sided shape

Properties Of Trapezoid:

1. A Quadrilateral is a trapezoid if and only if when the adjacent angles are supplementary (means sum of adjacent angles are 180 degrees).
2. In an isosceles trapezoid the base angles have same measure.
3. The bases (top and bottom) Trapezoid are parallel.
4. In an isosceles trapezoid the diagonals are concurrent.

Formulas For Trapezoid:

Area Of trapezoid= ½ (h(B+b))

Where B=length of longer base

B=length of smaller base

explain Definition of Quadrilaterals , what is the Definition of Quadrilaterals , Definition of Quadrilaterals with examples