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Exploring Polygons: Definitions, Types, and Interior Angles in 7th Grade Math

Dive into the fascinating world of polygons, essential concepts for 7th-grade math! Discover what defines a polygon, focusing on its three pivotal criteria: having three or more line segments, being a closed figure, and ensuring that line segments do not cross. Learn about various types of polygons, including regular and irregular shapes, and explore the names and characteristics of polygons with up to ten sides. Finally, master the formula to calculate the sum of interior angles, enhancing your mathematical skills and knowledge of geometry.

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Exploring Polygons: Definitions, Types, and Interior Angles in 7th Grade Math

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  1. POLYGONS Poly = “MANY” Gon = “ANGLES” OR “SIDES” 7th Grade Math

  2. POLYGONS!1. Three (3) or more line segments2. CLOSED figure3. Line segments DO NOT cross or intersect

  3. Polygon Examples:Do these meet the above 3 criteria?

  4. Is this shape a polygon? Why or why not?

  5. This shape is NOT “closed.”

  6. Why can’t a polygon have only 2 sides?

  7. With only 2 sides, the shape could not be “closed.”

  8. Is this shape a polygon?Does it meet the 3 criteria?

  9. YES, this IS a polygon.

  10. This shape is two-dimensional, “closed”, has 12 sides, and lines do not intersect.

  11. However, this is a special type of polygon called “concave.”

  12. It’s called “concave” because some of the sides are “caved in.”

  13. For our purposes, we will be discussing only convex polygons, not concave polygons.

  14. REGULAR Polygon…1. ALL sides congruent2. ALL angles congruentExample: Square and Equilateral TriangleWhat would it mean if I said, “I have a regular pentagon”?

  15. Let’s learn the names for the first eight polygons.

  16. Polygons!

  17. A one-sided polygon is called…?

  18. Trick question!!!There is no such thing as a one-sided polygon. Remember, polygons must have at least 3 sides.

  19. 3-sided polygon…TRIANGLE.

  20. You can remember the prefix “tri” by thinking of a tricycle. A tricycle has 3 wheels.

  21. 4-sided polygon… QUADRILATERAL.

  22. You can remember the prefix “quad” by thinking “times four.” Quadruple means x 4

  23. 5-sided polygon…PENTAGON

  24. You can remember this name by thinking about the building in Washington, D.C.

  25. 6-sided polygon…HEXAGON

  26. You can remember that a hexagon has six sides because the words hexagon and six both have the letter “x.”

  27. The hexagon is the polygon of choice for bees.

  28. 7-sided polygon…HEPTAGON.

  29. You can remember the prefix “hept” by thinking of the heptathalon in the Olympics. • heptathlon—a two-day event in which athletes compete SEVEN DIFFERENT EVENTS. • 100-meter hurdles • high jump • shot put • 200-meter dash • long jump • Javelin • 800-meter race on the second day.

  30. Joyner-Kersee, JackieJackie Joyner-Kersee, an American track-and-field athlete, who won the heptathlon event (an all-around event) at the Olympic Games in 1988 and 1992. She is considered one of the greatest female athletes.

  31. 8-sided polygon…OCTAGON

  32. You can remember the prefix “oct” by thinking of an octopus (that has 8 legs).

  33. 9-sided polygon…NONAGON

  34. You can remember that a nonagon has nine sides because the words nonagon and nine both have two “ns.”

  35. 10-sided polygon…DECAGON

  36. You can remember the prefix “dec” by thinking about a decade, which has 10 years. 2000 1999 1998 1997 1996 1995 TEN YEARS 1994 1993 1992 1991

  37. Sum of Interior Angles Discuss the angle measures for: Can you create a formula that would work?

  38. Formula to calculate the total degrees in a polygon:n = number of sides(n-2)180

  39. Scholastic “Sum of Interior Angles” Activity

  40. Practice:Glencoe Page 549 #1-5 #7-16

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