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# Polygons

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### Transcript

• 1. POLYGONS
• 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. Naming Polygons
B
A
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.
• 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.
• 29. EQUIANGULAR POLYGON
EQUILATERAL POLYGON
REGULAR POLYGON
Concept Emphasis
• 30. EQUILATERAL but not EQUIANGULAR
EQUILATERAL and EQUIANGULAR

EQUILATERAL and EQUIANGULAR
EQUILATERAL but not EQUIANGULAR