A polygon is defined as a plane figure formed by three or more line segments that intersect only at their endpoints. It must be a closed region. Regular polygons have equal side lengths and equal interior angles, while equilateral polygons only have equal side lengths. Convex polygons are those where any segment joining two interior points lies entirely within the polygon, while concave polygons contain at least one interior angle greater than 180 degrees.

2. polygon not a polygon

3. What is a polygon?
• 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”

4. Polygon or Not a Polygon?

5. Polygon or Not a Polygon?
Polygon

6. Polygon or Not a Polygon?

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

8. Polygon or Not a Polygon?

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

10. Polygon or Not a Polygon?

11. Polygon or Not a Polygon?
Polygon

12. Polygon or Not a Polygon?

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

14. Polygon or Not a Polygon?

15. Polygon or Not a Polygon?
Polygon

16. Polygon or Not a Polygon?

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

18. Regions in a Polygon

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

20. Parts of a Polygon
• Diagonals
▫ A diagonal of a polygon is any segment that joins
two nonconsecutive vertices. Figure shows five-
sided polygon QRSTU. Segments QS , SU , UR
, RT and QT are the diagonals in this polygon.

21. ALL POLYGONS

22. ALL POLYGONS???

23. ALL POLYGONS!

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

25. Convex Polygons Concave Polygons

26. 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.

27. Convex or Concave?
Convex

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

29. Convex or Concave?
Convex

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

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

32. Convex or Concave?
Convex

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

34. A B
D C
 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.

35. • Think of words beginning
with the prefixes tri-
, quad-, pent-, and oct-.
• Examples:
triathlon, quadriplegic, pen
tameter, and octopus.
• Meanings? (words and
prefixes)

36. 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

37.  EQUIANGULAR POLYGON
 EQUILATERAL POLYGON
 REGULAR POLYGON

38. EQUILATERAL but not EQUILATERAL and
EQUIANGULAR EQUIANGULAR
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EQUILATERAL and
EQUIANGULAR but not EQUIANGULAR
EQUILATERAL
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