POLYGONSPOLYGONSPoly = “MANY”Gon = “ANGLES” OR “SIDES”

7th Grade Math

POLYGONS!POLYGONS!

1. Three (3) or more line 1. Three (3) or more line segmentssegments2. CLOSED figure2. CLOSED figure3. Line segments DO NOT3. Line segments DO NOT

cross or intersect cross or intersect

Polygon ExamplesPolygon Examples::

Do these meet the above 3 Do these meet the above 3 criteria?criteria?

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

This shape is NOT This shape is NOT “closed.”“closed.”

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

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

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

YES, this IS a polygon.YES, this IS a polygon.

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

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

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

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

REGULAR PolygonREGULAR Polygon……

1. ALL sides congruent1. ALL sides congruent2. ALL angles congruent2. ALL angles congruent

ExampleExample: : Square and Equilateral Square and Equilateral TriangleTriangle

What would it mean if I said, What would it mean if I said, “I have a regular pentagon”?“I have a regular pentagon”?

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

Polygons! Polygons! Polygon Name

Picture Definition Prefix & Memory Device

A one-sided polygon is A one-sided polygon is called…?called…?

Trick question!!!Trick question!!!

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

3-sided polygon…3-sided polygon…

TRIANGLE.TRIANGLE.

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

                                

4-sided polygon…4-sided polygon…

QUADRILATERAL.QUADRILATERAL.

You can remember the prefix You can remember the prefix “quad” by thinking “times “quad” by thinking “times four.”four.”

Quadruple means x 4

5-sided polygon…5-sided polygon…

PENTAGONPENTAGON

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

6-sided polygon…6-sided polygon…

HEXAGONHEXAGON

You can remember that a You can remember that a hexagon has six sides hexagon has six sides because the words because the words hehexxagonagon and and sisixx both both have the letter “have the letter “xx.” .”

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

7-sided polygon…7-sided polygon…HEPTAGON.HEPTAGON.

You can remember the prefix You can remember the prefix “hept” by thinking of the “hept” by thinking of the heptathalon in the Olympics.heptathalon in the Olympics.

heptathlon—a two-day event in which athletes compete SEVEN DIFFERENT EVENTS.

1. 100-meter hurdles

2. high jump

3. shot put

4. 200-meter dash

5. long jump

6. Javelin

7. 800-meter race on the second day.

Joyner-Kersee, JackieJoyner-Kersee, Jackie

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

8-sided polygon…8-sided polygon…

OCTAGONOCTAGON

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

9-sided polygon…9-sided polygon…

NONAGONNONAGON

You can remember that a You can remember that a nonagon has nine sides nonagon has nine sides because the words because the words nnoonnagonagon and and nniinnee both both have two “have two “nnss.”.”

10-sided polygon…10-sided polygon…

DECAGONDECAGON

You can remember the prefix You can remember the prefix “dec” by thinking about a “dec” by thinking about a decade, which has decade, which has 1010 years. years.

19911992

19931994

19951996

19971998

19992000

TEN YEARS

Sum of Interior AnglesSum of Interior AnglesDiscuss the angle measures for:

Can you create a formula that would work?

Shape # of sidesHow many triangles in this

shape from one vertex?Degrees in a triangle? Degrees in Shape?

Triangle 3 1 180 180

Quadrilaterial

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Formula to calculate the Formula to calculate the total degrees in a total degrees in a

polygon:polygon:

nn = number of sides = number of sides

((nn-2)180-2)180

Scholastic “Sum of Interior Scholastic “Sum of Interior Angles” ActivityAngles” Activity

Practice:Practice:

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