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

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

##
**Sum of Interior Angles of Quadrilateral**

**(n-2) Χ**

**180**where n=the number of sides the shape has. A quadrilateral has four sides so

(4-2) Χ 180

= 2 Χ 180

= 360

∠1 + ∠2 ∠3 + ∠4 = 360°

## Types of Quadrilaterals

### Concave Quadrilaterals

A quadrilateral that contains a reflex angle.

#### 1. Parallelogram

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

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

*A rhombus is a parallelogram whose all four sides are equal*

####
**3. Rhomboid**

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

####
**4. Rectangle [Equiangular Quadrangle]**

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

####
**5. Square {Regular Quadrilateral}**

*A square is a rhombus whose all angles are right angles*

####
**6. Oblong**

*A oblong is a rectangle which has unequal adjacent sides.*

####
**7. Kite**

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

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

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

###
**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 + d = 180°

(b)

i.e. e = c

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

opposite angleopposite 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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