1. POLYGONS!
gone!
Polly

2. What is a polygon?
The term POLYGON means "many-angled" (Poly = many) & (Gon = angles) 
By definition A Polygon is:
a closed figure formed by a finite number of coplanar segments such that
the sides that have a common endpoint are noncollinear and
each side intersects exactly two other sides, but only at their endpoints
                            
 Wow that is pretty technical does that make sense to you?.... basically a polygon is a closed shape that is made up of line segments (no curves) and of course sides can only touch at the endpoints                       
Does that make more sense?  
POLYGONS
Non Polygons

3. Polygons are classified according to the number of sides they have.
A polygon is a closed plane figure bounded by straight line segments. The line segments are called the sides of the polygon, and the points at which they intersect are called vertices. A polygon has the same number of sides as it has vertices.
Polygons are classified according to the number of sides they have.
What is a three-sided polygon called?
What is a four-sided polygon called?

4. Other polygons
Name these other
polygons.

5. Click here to see
some more polygon
names

6. Name the polygons.

7. What kinds of polygons do you see?

8. Math is everywhere!
Name the polygons that
you see.

9. polygon art:
polygons?

10. What kind of triangle is regular?
If all the sides and all the angles of a polygon are congruent the polygon is said to be regular.
What kind of triangle is regular?
What kind of quadrilateral is regular?
Equilateral
triangle
square
pentagon
hexagon
octagon
decagon
heptagon
nonagon

11. A polygon that is not regular is irregular.

12. Concave and Convex polygons
A concave polygon is 'caved' in - some of its sides are bent inward.  For example the red and green shape are both concave polygons. 
An easy way to determine whether a shape is concave or not is the SEGMENT TEST.  If you can draw a straight segment between two points in the shape but part of the segment leaves the shape then the shape is concave.  
A convex polygon is the opposite of concave - when the segment test fails for all segments in the shape.  A more formal way of defining convex is a polygon such that no line containing a side of the polygon contains a point in the interior of the polygon.
concave
convex

13. Convex or Concave? 1.
convex 2.
concave 4. 3. 5. 6.

14. take a quick polygon quiz.
Test yourself!
Click on the button to
take a quick polygon quiz.
QUIZ

15. diagonals A diagonal is a segment drawn from one vertex
to another that is not a side.
Some diagonals:
All of the diagonals in a convex polygon will lie
inside the polygon.
At least one diagonal in a concave polygon will lie outside of the polygon.

16. Interior Angles The interior angles in a polygon are formed by
the sides.
Interior angle
The number of interior angles is equal to the number of sides and number
of vertices in the polygon.

17. What is the sum of the measures of the interior angles in
in a triangle is ____________.
in a convex quadrilateral is _____________.
What is the sum of the measures
of the interior angles in
any convex polygon?

18. Make a table to look for a pattern.
Polygon
name
Number of sides
# of diagonals drawn from one vertex
# of triangles formed
Sum of measures of interior angles
triangle
quadrilateral 5 6 7 8 9 n 3 1
180
360 4 1 2
pentagon 2
540 3
180
180
180
180
180

19. Formula for finding the sum of the measures of the interior
angles in a convex polygon:
(n - 2) 180
n = number of sides

20. Exterior angles Exterior angles are formed by extending a
side of the polygon.
exterior angle
exterior angle
exterior angle
exterior angle

21. exterior angles of a polygon?
What is the sum of the
exterior angles of a polygon?
(that means one exterior angle at each vertex)
360°
Sum of exterior angles =
120°
60°
TRIANGLE
120°
60°
60°
120°

22. 360° 360° 110° 120° 120° 95° 95° Sum of exterior angles =
QUADRILATERAL
PENTAGON
360°
Sum of exterior angles =

23. angles of any convex polygon (one angle at each vertex) is . . .
The sum of the exterior
angles of any convex polygon
(one angle at each vertex) is . . .
360°

24. take a quick polygon quiz.
Test yourself!
Click on the button to
take a quick polygon quiz.
QUIZ

25. Helpful polygon websites:
Definitions / examples
Polygon definition
Regular / irregular
Click on the button
to go to a website.
“textbook”
Geometry home page
Venn diagrams