Geometry: Polygons

Polygons

by Mr. Fisher

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As you progress through geometry, you will need to be able to identify polygons.

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You will be using formulas to find dimensions of polygons, but there are different formulas depending on the shape. Identifying the shape is an important part of selecting the right formula.

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Building blocks

​A single point is just a point.

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We can use two points to create a line.

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​We can use lines to create a square

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​We can use squares to create a cube.

What is a "dimension"?

A dimension is a direction we can measure in such as ...

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​How tall is it?

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​How wide is it?

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​How thick is it?

What about 2-dimensions and 3-dimensions?

A 2-dimensional object can be measured in two directions

​(height and width).

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​A 3-dimensional object can be measured in three directions (height, width, depth).

For this lesson, we are going to look at 2-dimensional shapes ...

​A polygon is ...

​Any flat, closed shape made from straight lines.

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​Flat -- 2-dimensional only

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​Closed -- Lines meet (no openings)

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​Straight lines -- No curves

Poll

How many polygons do you see in this bicycle?

• None

• One

• Two

• Three

• More than three!

I see three ...

​Why not?

• ​Tires

• ​Spokes

• ​Reflectors

Multiple Choice

A shape must have three qualities to be a polygon.

First, it must be ...

• 2-dimensional

• 3-dimensional

Multiple Choice

Second, a polygon must be ...

• Open

  (it has an opening)

• Closed

  (lines enclose a space inside)

Multiple Choice

Third, a polygon can only be made from ...

• Dots

• Curved lines

• Wavy Lays and

  hot fries

• Straight lines

​Next step ... What kind of polygon?

​*Regular vs. Irregular

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*How many sides?

​REGULAR polygons

​In other words ...

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​... the sides are all the same length ...

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​... and the inside angles are all the same.

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​IRREGULAR polygons

Irregular polygons meet all the conditions for a polygon (flat, closed, straight lines) but have lines or angles that are not equal.

​We can use formulas to find unknown measurements of regular polygons

and shapes.

​(Quick check on the next slide

-- why isn't that circle a polygon?)

Multiple Choice

Why is a circle NOT a polygon?

• It is a polygon!

• It does not have straight lines.

• It is not flat (or

  2-dimensional).

• The circle never got AROUND to becoming a polygon!

  (Get it?)

​To choose the right formula, you need to know which polygon you are working with.

The basic ones we will work with are:

• ​Triangle

• ​Parallelogram

​TRIANGLES

• Triangles have three sides

• ​Triangles are half of a parallelogram!