Polygons are plane figures bounded by three or more straight sides that meet at vertices. Polygons are classified as convex or concave based on whether a line segment between two interior points crosses two or more sides. They are also classified by the number of sides, with triangles having three sides, quadrilateral four sides, and so on. Regular polygons are both equilateral and equiangular. The interior angles of a triangle sum to 180 degrees, while the interior angles of a quadrilateral sum to 360 degrees.

1. POLYGONS

2. POLYGONS
a closed plane figure
bounded by three or more
straight sides that meet in
pairs in the same number of
vertices, and do not intersect
other than at these vertices.

3. CLASSIFICATION OF POLYGONS
Polygons first fit into two general
categories— convex and not convex
(sometimes called concave).
A polygon is concave if there are two
points somewhere inside it for which a
segment with these as its endpoints cuts at
least 2 of the sides of the polygon.
A polygon that is not concave is called
convex

4. CLASSIFICATION OF POLYGONS
Figure 1 shows some convex polygons, some non-convex polygons, and
some figures that are not even classified as polygons.

5. CLASSIFICATION OF POLYGONS
Polygons are also classified by how many sides (or angles) they have.
The following lists the different types of polygons and the number of
sides that they have:
A triangle is a three-sided polygon
A quadrilateral is a four-sided polygon.
A pentagon is a five-sided polygon.
A hexagon is a six-sided polygon.
A septagon or heptagon is a seven-sided polygon.
An octagon is an eight-sided polygon.
A nonagon is a nine-sided polygon.
A decagon is a ten-sided polygon

6. REGULAR POLYGONS
When a polygon is both equilateral and equiangular, it is referred to as a regular
polygon. For a polygon to be regular, it must also be convex.
Figure 5
shows examples of regular polygons.

7. PARTS OF A POLYGON
- The endpoints of the sides of polygons are called vertices. When naming a polygon,
its vertices are named in consecutive order either clockwise or counterclockwise.
- Consecutive sides are two sides that have an endpoint in common. The four-sided
polygon in Figure 2 could have been named ABCD, BCDA, or ADCB, for example.
It does not matter with which letter you begin as long as the vertices are named
consecutively. Sides AB and BC are examples of consecutive sides.
Figure 2 There are four pairs of consecutive sides in this polygon.

8. PARTS OF A POLYGON
A diagonal of a polygon is any segment that joins two nonconsecutive vertices.
Figure 3 shows five-sided polygon QRSTU. Segments QS , SU , UR , RT and QT are
the diagonals in this polygon.
Figure 3
Diagonals of a polygon.

9. SUM OF THE INTERIOR ANGLES OF A POLYGON
An Interior Angle is an angle inside a shape.

10. TRIANGLES
The Interior Angles of a Triangle add up to 180
90 + 60 + 30 = 180 80 + 70 + 30 = 180

11. QUADRILATERALS
A Quadrilateral is any shape with 4 sides
90 + 90 + 90 + 90 = 360 80 + 100 + 90 + 90 = 360
A Square adds up to 360
The Interior Angles of a Quadrilateral add up to 360