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

*A quadrilateral is a polygon with four sides (edges) or four vertices or four corners*

*it can also be called as a TETRAGON*

After reading this tutorial you can answer these questions like

## What are the properties of quadrilateral?

## What is a diagonal and what are adjacent sides?

## How many types of quadrilaterals are there in Geometry?

## What is a cyclic quadrilateral and what are its properties?

## And at last but not the least all types and properties of parallelogram, rhombus, square, rectangle, kite, oblong, trapezoid, etc.

##
**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__:-

*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__:-

__Adjacent Sides__:-

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

- AD and DC
- DC and BC
- BC and AB
- AB and AD

###
__Adjacent Angles__:-

__Adjacent Angles__:-

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

- ∠1 and ∠3
- ∠3 and ∠4
- ∠2 and ∠4
- ∠1 and ∠2

### Types of Quadrilaterals

**square**,

**rhombus**and

**rectangle**are also

**.**

*parallelograms*### Concave Quadrilaterals

####
**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.

####
**8. Trapezoid (Trapezium)**

####
** ***A quadrilateral with at least one pair of parallel sides is known as a trapezoid*

*A quadrilateral with at least one pair of parallel sides is known as a trapezoid*

####
**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**

**cyclic quadrilateral**

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

*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:**

**the opposite angles of a cyclic quadrilateral sum to 180°**

b + d = 180°

**the exterior angle of a cyclic quadrilateral is equal to the interior**

opposite angle

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 |

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