Types of Quadrilaterals and Their Properties: Different types of quadrilaterals are explained below with their properties. Types of polygons and Types of Quadrilaterals with Properties of kite Quadrilateral are also explained.
Here, ABCD is a quadrilateral.
AD and BC are diagonals.
Different Types of Quadrilaterals and Their Properties
The quadrilateral with all-sided equal and every angle equal to the right angle is a square. Diagonals of a square are equal in length and cut each other at 90°.
Square diagonals are equal
BD=AC = √2 × SIDE
AC and BD bisect each other at O.
Angles of a square are equal and 90°. (Each angle)
Square is a special kind of rhombus and rectangles. All the properties of the rhombus and rectangle will be satisfied for the square.
The quadrilateral with opposite sides length equal and every angle equal to 90˚ is a rectangle.
Here ABCD is a rectangle.
∠A = ∠B = ∠C = ∠D = 90° (Each angle)
AC2 = AB2 + BC2 = BD2 = BC2 + CD2
Diagonals AC and BD bisect each other at 90°.
Rhombus is a special kind of square with all sides equal, opposite sides parallel, and diagonals bisect each other at 90°.
ABCD is a rhombus.
Opposite angles are equal.
∠A=∠C and ∠B=∠D
Adjacent angles sum is equal to 180°
∠A + ∠B = 180° = ∠B + ∠C = ∠C + ∠D = ∠D + ∠A
Diagonals bisect each other at 90°
AD = OC and BO = OD
∠AOB = ∠BOC = ∠COD = ∠DOA = 90°
A parallelogram is a special kind of rectangle with opposite sides parallel and equal in length, opposite angles are equal, adjacent angles sum equal to 180°, and diagonals bisect each other.
Adjacent angles sum equals to 180°
∠A + ∠D = ∠D + ∠C = ∠C + ∠B = ∠B + ∠A = 180°
Opposite angles are equal.
∠A = ∠C; ∠D = ∠B.
Diagonals bisect each other at “O”
OA = OC and OB = OD but AC || BD.
The quadrilateral in which a pair of opposite sides are parallel to each other but they are not equal, that is a trapezium.
ABCD is a trapezium.
AB ||CD but AB≠CD.
The Sum of all the angles equals 380°.
Diagonals bisect each other.
OD = OB and AO = OC.
Properties of Kite Quadrilateral
Kite Quadrilateral Sides
Two pairs of sides have equal sides and these sides are adjacent to each other.
AB = AD is one pair of sides and AB, AD adjacent to each other.
BC = CD is another pair of sides and BC, CD are adjacent to each other.
Kite Quadrilateral Angles
Angles formed by these two pairs of sides are equal.
∠B = ∠D
Kite Quadrilateral Diagonals
Diagonals bisect each other at right angles.
OA = OC
OB = OD
Properties of Quadrilateral
Polygon is a 2-dimensional shape bounded by three or more finite number of straight lines. Depending on the number of polygons. For a regular polygon, all the sides are equal.
Types of Polygons
These are two types of polygons. They are regular polygons and irregular polygons.
Angles in a Polygon
- The Sum of all the exterior angles of a polygon is equal to 360°.
- Each exterior angle of a polygon = 360° / number of sides of the polygon
(360°/6) = 60°
Each exterior angle of the hexagon is 60°.
The Interior angle is an angle formed by two sides of a polygon that share one common point as vertices.
The Sum of an interior angle and exterior angle is equal to 180°.
So, interior angle = 180° – exterior angle.
ABCDEF is a regular hexagon of sides ‘6’.
Interior angles are A, B, C, D, E, and F.
Interior angle = 180° – (360°/n).
Here ‘n’ is ‘6’.
Interior angle = 180° – (360/6) °
= 180° – 60°
Each interior angle of the hexagon is 120°.
Properties of Regular Polygons
* ‘n’ is number of sides of the polygon
- Each exterior angle of polygon = (360°/n) or [180° – (Each interior angle)]
- Each exterior angle of a polygon = [(n-2)×180°]/n (or) [180° – (each exterior angle)]
(or) [180° – (360°/n)]
- Sum of interior angles of a polygon is (n-2) × 180°
- The Sum of exterior angles of a polygon is (n-2) × 180° / n.
- Number of diagonals of a polygon is [n×(n-3)] / 2.
- Each angle at the center formed by the intersection of lines from any side of a polygon is 360°/n.
Area of Polygon
Let polygon be of ‘n’ sided.
- Area of a polygon = (na2 /4 )×cot(/n).
- The radius of inner circle of a polygon is (r)
( a/2)× cot (180°/n)
- The radius of outer circle of a polygon is (a/2) × cosec (180°/n)
Circumcircle, In-Circle, Radius, and Apothem of Polygon
- The outside circle of a polygon is circumcircle. ‘R’ is the circumradius.
- Circum circle is formed by touching all the vertices in the polygon.
In-Circle of Polygon
- Inside circle of a polygon is called in-circle. ‘r’ is the radius of the circle.
- In the circle is formed by touching all the sides of the polygon
- The radius of the circle is also called the apothem.