polygons “many” “sides”. a polygon is a 2-dimensional shape
TRANSCRIPT
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POLYGONS“MANY” “SIDES”
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A polygon is a 2-dimensional shape.
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This means that polygons have both length and width.
WIDTH
L
E
N
G
T
H
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Polygons are closed shapes, and they are made of at least 3 line
segments (straight lines).
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Why is this shape NOT a polygon?
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This shape is NOT “closed.”
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Why can’t a polygon have only 2 sides?
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With only 2 sides, the shape could not be “closed.”
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Is this shape a polygon?
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As a matter of fact, this IS a polygon.
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This shape is “closed,” and it has 12 sides.
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However, this is a special type of polygon called “concave.”
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It’s called “concave” because some of the sides are “caved in.”
and you can draw a line segment outside of the figure when
connecting two vertices.
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For our purposes, we will be discussing only convex polygons
and not concave polygons.
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We will learn the names for the first eight polygons.
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A one-sided polygon is called…?
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That’s a trick question. There is no such thing as a one-sided
polygon. Remember, polygons must have at least 3 sides.
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A 3-sided polygon is called a triangle.
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You can remember the prefix “tri” by thinking of a tricycle. A
tricycle has 3 wheels.
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A 4-sided polygon is called a quadrilateral.
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You can remember the prefix “quad” by thinking “times four.”
Quadruple means x 4
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A 5-sided polygon is called a pentagon.
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You can remember this name by thinking about the building in
Washington, D.C.
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A six-sided polygon is called a hexagon.
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You can remember that a hexagon has six sides because the words hexagon and six both have
the letter “x.”
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The hexagon is the polygon of choice for bees.
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A 7-sided polygon is called a heptagon.
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An 8-sided polygon is called an octagon.
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You can remember the prefix “oct” by thinking of an octopus.
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A 9-sided polygon is called a nonagon.
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You can remember that a nonagon has nine sides because
the words nonagon and nine both have two “ns.”
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A 10-sided polygon is called a decagon.
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You can remember the prefix “dec” by thinking about a
decade.
19911992
19931994
19951996
19971998
19992000
TEN YEARS
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Let’s explore the diagonals of a polygon.
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Diagonals from 1 vertex of a quadrilateral.
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Diagonals from 1 vertex of a pentagon.
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Diagonals from 1 vertex of a hexagon.
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None, this is a trick question
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Another interesting characteristic of TOTAL diagonals in polygons:
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A diagonal in a polygon connects two vertices (corners).
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A quadrilateral has 2 total diagonals.
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A pentagon has 5 total diagonals.
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A hexagon has 9 total diagonals.
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Now let’s chart our findings and look for a pattern.
Polygon Total Number of Diagonals
3 (Triangle) 0
4 (Quadrilateral) 2
5 (Pentagon) 5
6 (Hexagon) 9
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Now let’s chart our findings and look for a pattern.
Polygon Total Number of Diagonals
3 (Triangle) 0
4 (Quadrilateral) 2
5 (Pentagon) 5
6 (Hexagon) 9
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Here’s the formula:
Total diagonals =
Number of vertices X
Diagonals from a single vertex÷ 2
T = n x (n 3)
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Using the formula try finding the number of total diagonals in a regular decagon:
• T = n x (n 3)
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This concludes my show on polygons.
The End.