A polygon is defined as a closed plane figure formed by three or more segments that intersect only at their endpoints. Polygons are categorized as convex, where any line segment joining two points remains inside, or concave, where such segments can extend outside the polygon. Additionally, polygons are named based on the number of their sides, ranging from triangle (3 sides) to dodecagon (12 sides).

1. PO
LYGO
N
S

2. polygon not a polygon

3. • A polygon is a plane figure.
• A polygon is a closed region.
• A polygon is formed by three or more
segments as its sides.
• Each side of a polygon intersects only
one segment at each of its endpoints.
• poli + gonus  “many angled”
What is a polygon?

4. Polygon or Not a Polygon?
Polygon

5. Polygon or Not a Polygon?
Not Polygon
because sides are not
segments.

6. Polygon or Not a Polygon?
Not Polygon
because sides are
intersecting not just
at the endpoints.

7. Polygon or Not a Polygon?
Polygon

8. Polygon or Not a Polygon?
Not Polygon
because sides are
intersecting not just
at the endpoints.

9. Polygon or Not a Polygon?
Polygon

10. Polygon or Not a Polygon?
Not Polygon
because sides are
intersecting more
than one other side at
its endpoint.

11. Regions in a Polygon

12. Parts of a Polygon
• sides
▫ consecutive sides
 included angle
▫ nonconsecutive sides
• interior angles / vertex angles
▫ consecutive angles
 included side
▫ nonconsecutive angles
• exterior angles
• diagonals

13. ALL POLYGONS

14. ALL POLYGONS???

15. ALL POLYGONS!

16. How can these polygons be divided into two groups?

17. Convex Polygons Concave Polygons

18. Polygon Convexity
A polygonal region is convex if any
segment joining any two points of the
polygon is part of the interior region.
If a polygon is not convex, then its is
concave.

19. Convex or Concave?
Convex

20. Convex or Concave?
Concave
because a segment
connecting points on
the polygon that will
lie in the exterior can
be drawn.

21. Convex or Concave?
Convex

22. Convex or Concave?
Concave
because a segment
connecting points on
the polygon that will
lie in the exterior can
be drawn.

23. Convex or Concave?
Concave
because a segment
connecting points on
the polygon that will
lie in the exterior can
be drawn.

24. Convex or Concave?
Convex

25. Convex or Concave?
Concave
because a segment
connecting points on
the polygon that will
lie in the exterior can
be drawn.

26.  Polygons are named by writing their consecutive
vertices in order, such as ABCD or CDAB for the
polygon above.
 We cannot name the polygon as DBAC.
NAMING POLYGONS
B
A
C
D

27. Connecting to Prior Knowledge
• Think of words beginning
with the prefixes tri-,
quad-, pent-, and oct-.
• Examples: triathlon,
quadriplegic, pentameter,
and octopus.
• Meanings? (words and
prefixes)

28. Polygons can be named by their number of sides.
Number of Sides Name of Polygon
3 triangle
4 quadrilateral
5 pentagon
6 hexagon
7 heptagon
8 octagon
9 nonagon
10 decagon
11 undecagon
12 dodecagon

29.  EQUIANGULAR POLYGON
 EQUILATERAL POLYGON
 REGULAR POLYGON
Concept Emphasis

30. EQUILATERAL but not
EQUIANGULAR
REGULAR
EQUIANGULAR but not
EQUILATERAL
REGULAR
┌
┌
┌
┌
┌
┌
┌
┌