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Maths Exercices

Polygons

Polygons are closed plane figures formed by three or more line segments. These line segments are called the sides or edges of the polygon.

Polygons
Non polygons

A figure or shape is not considered a polygon if it has rounded sides or if its sides intersects at any place other than at the ends of each side.

Vertices
The endpoints of each side of a polygon are called vertices (plural of vertex). We name a polygon by assigning a letter to each vertex, proceeding in alphabetical order.

The vertices of this four-sided polygon are A, B, C, and D. So the polygon can be defined by ABCD.

Consecutive sides
Any two sides that share a common vertex are called consecutive sides.

This polygon has four pairs of consecutive sides. They are and , and , and , and and .

Diagonal
A line segment that joins any two nonconsecutive vertices of a polygon is a diagonal.

The polygon ABCD contains diagonals and


Regular polygons
Regular polygon is a polygon where all sides are of equal length, called equilateral sides, and where all angles are also equal, called equilateral angles.

Some regular polygons are so common that they have a special descriptive mathematical name:

Number of sides
Common name
3
Triangle
4
Square (Quadrilateral)
5
Pentagon
6
Hexagon
7
Heptagon
8
Octagon
9
Nonagon
10
Decagon
12
Dodecagon
n
n-gon

Concave and convex polygons
A polygon is convex if and only if the line segment connecting any two points in the polygonal region lies entirely within the region. If a polygon is not convex, it is called concave or nonconvex.

Convex polygons
Concave polygons

A convex polygon has all diagonals within the figure. Also all interior angles are less than 180º.

A concave polygon (caves in) has at least one diagonal outside the figure. Also, at least one interior angle is greater than 180º.


Congruent polygons
Polygons are congruent when they have the same number of sides, and all corresponding sides and interior angles are congruent. The polygons will have the same shape and size, but one may be a rotated, or be the mirror image of the other.

In the figure below, all the irregular pentagons shown are congruent.
(The darker ones are mirror images of the others)