Lesson 1.1: POLYGON
• A polygon is a closed plane figure that is joined by line segments.
• A polygon may also be defined as a union of line segments such that:
i) each endpoint is the endpoint of only two segments;
ii) no two segments intersect except at an endpoint; and
iii) no two segments with the same endpoint are collinear.
Types of Polygon
• Regular Polygon.
In a regular polygon, all angles are equal and all sides are of the same length. Regular polygons are
both equiangular and equilateral.
• Equiangular Polygon.
A polygon is equiangular if all of its angles are congruent.
• Equilateral Polygon.
A polygon is equilateral if all of its sides are equal.
• Irregular Polygon.
A polygon that is neither equiangular nor equilateral is said to be an irregular polygon.
• Convex Polygon
Every interior angle of a convex polygon is less than 180°. If a line is drawn through the
convex polygon, the line will intersect at most two sides.
• Concave Polygon
A concave polygon has at least one interior angle that measures more than
180°. If a line is drawn through a concave polygon, the line may intersect
more than two sides.
,TENS – CONTA
HUNDREDS - HECTA
, We say that two polygons are similar if their corresponding interior angles are congruent and their
corresponding sides are proportional.
By ratio and proportion,
x1 y1
=
x2 y2
2
A 1 x1
=
A 2 x2 ( )
P1 x 1
=
P2 x 2
The altitude a of the triangle is called the apothem
The angle θ that is opposite the base of this triangle is called the central angle.
Perimeter: P=ns
360 °
Central Angle: θ=
n
s
Apothem: a=
2 tan ( 180 °/ n )
n=¿ no. of sides
• A polygon is a closed plane figure that is joined by line segments.
• A polygon may also be defined as a union of line segments such that:
i) each endpoint is the endpoint of only two segments;
ii) no two segments intersect except at an endpoint; and
iii) no two segments with the same endpoint are collinear.
Types of Polygon
• Regular Polygon.
In a regular polygon, all angles are equal and all sides are of the same length. Regular polygons are
both equiangular and equilateral.
• Equiangular Polygon.
A polygon is equiangular if all of its angles are congruent.
• Equilateral Polygon.
A polygon is equilateral if all of its sides are equal.
• Irregular Polygon.
A polygon that is neither equiangular nor equilateral is said to be an irregular polygon.
• Convex Polygon
Every interior angle of a convex polygon is less than 180°. If a line is drawn through the
convex polygon, the line will intersect at most two sides.
• Concave Polygon
A concave polygon has at least one interior angle that measures more than
180°. If a line is drawn through a concave polygon, the line may intersect
more than two sides.
,TENS – CONTA
HUNDREDS - HECTA
, We say that two polygons are similar if their corresponding interior angles are congruent and their
corresponding sides are proportional.
By ratio and proportion,
x1 y1
=
x2 y2
2
A 1 x1
=
A 2 x2 ( )
P1 x 1
=
P2 x 2
The altitude a of the triangle is called the apothem
The angle θ that is opposite the base of this triangle is called the central angle.
Perimeter: P=ns
360 °
Central Angle: θ=
n
s
Apothem: a=
2 tan ( 180 °/ n )
n=¿ no. of sides
