## Types of Numbers

### Natural numbers

(ℕ)

The counting numbers {1, 2, 3, …}, are called natural numbers. They include all the counting numbers i.e. from 1 to infinity.

### Whole numbers (w)

They are the natural numbers including zero. Not all whole numbers are natural numbers, but all natural numbers are whole numbers.

### Integers (Z)

Positive and negative counting numbers, as well as zero.

### Rational numbers (Q)

Numbers that can be expressed as a fraction of an integer and a non-zero integer.

### Real numbers (ℝ)

All numbers that can be expressed as the limit of a sequence of rational numbers. Every real number corresponds to a point on the number line.

### Irrational numbers

A real number that is not rational is called irrational.

### Complex Numbers (C)

Includes real numbers and imaginary numbers, such as the square root of negative one.

### Hypercomplex numbers (C)

Includes various number-system extensions: quaternions, octonions, tessarines, coquaternions, and biquaternions.

## Number representations

Decimal
The standard Hindu–Arabic numeral system using base ten.

Binary
The base-two numeral system used by computers.

Roman
The numeral system of ancient Rome, still occasionally used today.

Fractions
A representation of a non-integer as a ratio of two integers. These include improper fractions as well as mixed numbers.

Scientific Notation
A method for writing very small and very large numbers using powers of 10. When used in science, such a number also conveys the precision of measurement using significant figures.

Knuth’s up-arrow notation and Conway chained arrow notation
Notations that allow the concise representation of extremely large integers such as Graham’s number.

## Types and Properties of Quadrilaterals (Quadrangles)

#### A quadrilateral is a polygon with four sides (edges) or four vertices or four corners it can also be called as a TETRAGON

There are different types and varieties of quadrilaterals having different properties such as different angles and sides. You can learn them here in a very easy and informative way.

After reading this tutorial you can answer these questions like

## Properties of Quadrilaterals:

-Four sides.
-Four vertices (corners).
-Interior angles sum to 360°.
-Exterior angles sum to 360°.

## Important Terms Related to Quadrilateral:

### Diagonals:-

Diagonals are line segments that join two opposite vertices of a quadrilateral (corners).

A quadrilateral can have maximum two diagonal

Where AD is the line segment joining two opposite vertices A and D

### Adjacent Sides:-

Two sides are adjacent, if they share a common vertex.

In the quadrilateral shown above the 4 pair of adjacent sides are:

1.  AD and DC
2.  DC and BC
3.  BC and AB
4.  AB and AD

### Adjacent Angles:-

Two angles are adjacent, if they share a common side.

In the quadrilateral shown above the 4 pair of adjacent angles are:

1. ∠1 and ∠3
2. ∠3 and ∠4
3. ∠2 and ∠4
4. ∠1 and ∠2

### Types of Quadrilaterals

There are special types of quadrilateral:

Some types are also included in the definition of other types! For example a square, rhombus and rectangle are also parallelograms.

### Concave Quadrilaterals

A quadrilateral that contains a reflex angle.

#### 1. Parallelogram

A parallelogram is a quadrilateral with two pairs of parallel and equal sides

#### Properties of Parallelogram :-

• Opposite sides are congruent(i.e., Equal in length).
• Opposite angels are congruent(i.e., Equal in length).
• Consecutive angles are supplementary (i.e., Sum of consecutive angle = 180°).
• If one angle is right angle, then all angles are right angle(i.e., It is a square).
• The diagonals of a parallelogram bisect each other to form two pairs of congruent triangles.

#### 2. Rhombus (Rhomb) {Equilateral Quadrangle

A rhombus is a parallelogram all of whose all four sides are congruent

#### Properties of Rhombus :-

• All four sides are congruent(i.e., Equal in length).
• Opposite sides are parallel(i.e., It’s a parallelogram).
• Opposite angels are congruent(i.e., Equal in length).
• Consecutive angles are supplementary (i.e., Sum of consecutive angle = 180°).
• The diagonals of a rhombus bisect pairs of opposite angles.
• If one angle is right angle, then all angles are right angle(i.e., It is a square).
• Four congruent triangles are formed by diagonals.

#### 3. Rhomboid

A rhomboid is a parallelogram in which adjacent sides are of unequal lengths and oblique angles

#### Properties of Rhomboid :-

• All four sides are congruent(i.e., Equal in length).
• Opposite angels are congruent(i.e., Equal in length).
• Opposite angels are parallel(i.e., It’s a parallelogram).
• Consecutive angles are supplementary (i.e., Sum of consecutive angle = 180°).
• If one angle is right angle, then all angles are right angle(i.e., It is a square).
• The diagonals bisect each other to form two pairs of congruent triangles.

#### 4. Rectangle [Equiangular Quadrangle]

A rectangle is a plane figure with four straight sides and four right angles

Properties of Rhombus :-

• Opposite sides that are congruent and parallel.
• Adjacent sides are of unequal length
• Consecutive angles are supplementary, and
• Diagonals bisect each other.

#### 5. Square {Regular Quadrilateral}

A square is a rhombus whose all angles are right angles

#### Properties of Square :-

• The diagonals bisect each other and at right angle.
• The diagonals bisect its angles.
• Opposite sides parallel and congruent.
• All four angles square are congruent.
• All four sides square are congruent.
• The diagonals are congruent.

#### 6. Oblong

A oblong is a rectangle which has unequal adjacent sides.

#### Properties of oblong :-

• Two sets of parallel lines meeting at right angles.

#### 7. Kite

A kite is a quadrilateral whose two pair of adjacent sides are equal

#### Properties of Kites:-

• Two sets of parallel lines meeting at right angles.
• Two disjoint pairs of consecutive sides are congruent by definition   Note: Disjoint means that the two pairs are totally separate.
• The diagonals are perpendicular.
• One diagonal is the perpendicular bisector of the other diagonal
• The main diagonal bisects a pair of opposite angles.
• The opposite angles at the endpoints of the cross diagonal are congruent.

#### Properties of Kites:-

• The bases are parallel by definition.
• Each lower base angle is supplementary to the upper base angle on the same side.

## Cyclic Quadrilaterals

A cyclic quadrilateral (inscribed quadrilateral) is a quadrilateral drawn inside a circle so that its corners lie on the circumference of the circle

whose vertices all lie on a single circle. This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic. The center of the circle and its radius are called the circumcenter and the circumradius respectively. Other names for these quadrilaterals are concyclic quadrilateral and chordal quadrilateral, the latter since the sides of the quadrilateral are chords of the circumcircle.

### Properties of Cyclic Quadrilaterals:

(a) the opposite angles of a cyclic quadrilateral sum to 180°
i.e. a+ c = 180°
b + d = 180°
(b) the exterior angle of a cyclic quadrilateral is equal to the interior
opposite angle

i.e. e = c

Summary
Here is a list of all the properties of quadrilaterals that we have mentioned along with the classes of the quadrilaterals that possess those properties:
 Property Quadrilaterals Orthodiagonal Kite, Dart, Rhombus, Square Cyclic Square, Rectangle, Isosceles Trapezoid Inscriptible Kite, Dart, Rhombus, Square Having two parallel sides Rhombus, Square, Rectangle, Parallelogram, Trapezoid Having two pairs of parallel sides Rhombus, Square, Rectangle, Parallelogram Equilateral Rhombus, Square Equiangular Rectangle, Square