Chap 3 UNDERSTANDING QUADRILATERALS

Chap 3

UNDERSTANDING QUADRILATERALS

SOME IMPORTANT FACTS

1.       CURVE :Any drawing  done without lifting the pencil may be called a curve. In this sense , a line is also curve. A simple curve is one that does not cross  itself.

2.       CLOSED/ OPEN CURVE : A curve is said to be closed if its ends are joined ; otherwise it is said to be open.

3.       A polygon is a closed curve made up of line segments. Here ,

a)      The line segments are the sides of the polygon.

b)      Any two sides with common end points are called adjacent sides.

c)       The meeting point of a pair of sides is called a vertex.

d)      The end points of the same side are adjacent vertices.

e)      The line joining any two non adjacent vertices is a diagonal.

4.       CONVEX POLYGON : if each angle of a polygon is less than 180⁰ , it is called a convex polygon.

5.       CONCAVE OR RE-ENTRANT POLYGON : If at least one angle of a polygon is more than 180⁰  , it is called a concave or re-entrant polygon.

6.   Special types of Quadrilaterals :

a)   Square :  A Quadrilateral having all sides equal and each angle measuring 90⁰ is called a square.

b)      Rhombus : A parallelogram having all sides equal is called a Rhombus.

c)       Parallelogram : A Quadrilateral having its opposite sides parallel is called a Parallelogram

d)      Rectangle : A Quadrilateral having its opposite sides equal and each angle measuring 90⁰ is called rectangle.

e)      Trapezium : A Quadrilateral in which a pair of opposite sies is parallel is called a trapezium.

f)      Kite : A Quadrilateral having two pairs of equal adjacent sides, but unequal opposite sides, is called a kite.

g)     Special types of Triangles ( 3 Sides ) - right, equilateral, isosceles, scalene, acute, obtuse.

h)     Polygon Names
Generally accepted names

Sides	Name
n	N-gon
3	Triangle
4	Quadrilateral
5	Pentagon
6	Hexagon
7	Heptagon
8	Octagon
10	Decagon
12	Dodecagon

i)    Names for other polygons have been proposed.

Sides	Name
9	Nonagon, Enneagon
11	Undecagon, Hendecagon
13	Tridecagon, Triskaidecagon
14	Tetradecagon, Tetrakaidecagon
15	Pentadecagon, Pentakaidecagon
16	Hexadecagon, Hexakaidecagon
17	Heptadecagon, Heptakaidecagon
18	Octadecagon, Octakaidecagon
19	Enneadecagon, Enneakaidecagon
20	Icosagon
30	Triacontagon
40	Tetracontagon
50	Pentacontagon
60	Hexacontagon
70	Heptacontagon
80	Octacontagon
90	Enneacontagon
100	Hectogon, Hecatontagon
1,000	Chiliagon
10,000	Myriagon

j)        The number of diagonals in a polygon of n sides  =  

 [ n( n – 1) / 2  - n ], = 1/2 N(N-3)

k)      A polygon is said to a regular polygon , if all its ,

a)      Interior angles are equal;

b)      Sides are equal  and

c)      Exterior angles are equal.

l)        Each Interior Angle of a n sided regular polygon

= [ ( n – 2 ) x 180⁰]  

                         2

m)   Each Interior Angle of a n sided regular polygon  =   360⁰

  N

n)      Numbers of sides in a regular polygon   =       360⁰

    Exterior angle

o)      At each vertex of a polygon :

Interior angle + Exterior angle = 180⁰

p)      Angle sum property of a Quadrilateral : The sum of angles of a Quadrilateral is 360⁰.

q)      Sum of Exterior angles of a polygon : if the sides of a polygon are produced in order , the sum of exterior angles so formed is always 360⁰.

r)        

PolygonFormulas
(N = # of sides and S = length from center to a corner)

Area of a regular polygon = (1/2) N sin(360°/N) S²

Sum of the interior angles of a polygon = (N - 2) x 180°

The number of triangles (when you draw all the diagonals from one vertex) in a polygon = (N - 2)