MATHS HALF YEARLY NOTES
Underst anding Quadrilat erals
Plane Surface
A flat surface like paper is a plane surface.
Plane Curve
When we get a curve by joining the number of points without lifting the pencil is a
plane curve.
It could be an open or closed curve.
Open Curve
Closed Curve
Polygons
The simple closed curves which are made up of line segments only are called
the Poly gons.
Classifi cat ion of Polygons
Polygons can be classified by the number of sides or v ert ices they have.
Number of sides Name of Poly gon Figure
,3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
, 9 Nonagon
10 Decagon
n n-gon
Diagonals
Any line segment which connects the two non-consecutive vertices of a polygon is
called Diagonal .
Interior and Exterior of a Closed Curve
The blue shaded part represents the int erior and ext erior of the closed curve.
Convex and Concave Polygons
The polygons which have all the diagonals inside the figure are known as a Conv ex
Poly gon.
, The polygons which have some of its diagonals outside the figure also are known as
a Concav e Poly gon .
Regular and Irregular Polygons
Polygons which are equiangular and equilateral are called Regular Poly gons i.e. a
polygon is regular if-
It’s all sides are equal.
It’s all angles are equal.
Hence square is a regular polygon but a rectangle is not as its angles are equal but
sides are not equal.
Angle Sum Property
The sum of all the interior angles of a polygon remains the same according to the
number of sides regardless of the shape of the polygon.
The sum of interior angles of a polygon is-
Underst anding Quadrilat erals
Plane Surface
A flat surface like paper is a plane surface.
Plane Curve
When we get a curve by joining the number of points without lifting the pencil is a
plane curve.
It could be an open or closed curve.
Open Curve
Closed Curve
Polygons
The simple closed curves which are made up of line segments only are called
the Poly gons.
Classifi cat ion of Polygons
Polygons can be classified by the number of sides or v ert ices they have.
Number of sides Name of Poly gon Figure
,3 Triangle
4 Quadrilateral
5 Pentagon
6 Hexagon
7 Heptagon
8 Octagon
, 9 Nonagon
10 Decagon
n n-gon
Diagonals
Any line segment which connects the two non-consecutive vertices of a polygon is
called Diagonal .
Interior and Exterior of a Closed Curve
The blue shaded part represents the int erior and ext erior of the closed curve.
Convex and Concave Polygons
The polygons which have all the diagonals inside the figure are known as a Conv ex
Poly gon.
, The polygons which have some of its diagonals outside the figure also are known as
a Concav e Poly gon .
Regular and Irregular Polygons
Polygons which are equiangular and equilateral are called Regular Poly gons i.e. a
polygon is regular if-
It’s all sides are equal.
It’s all angles are equal.
Hence square is a regular polygon but a rectangle is not as its angles are equal but
sides are not equal.
Angle Sum Property
The sum of all the interior angles of a polygon remains the same according to the
number of sides regardless of the shape of the polygon.
The sum of interior angles of a polygon is-
