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8.10: Polygon Classification

Difficulty Level: At Grade Created by: CK-12
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Practice Polygon Classification
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Mustafa's parents are beekeepers. He watches them tend to the bees and get the honey. He sees patterns in the structure of the beehives and he notices that each hive tends to have the same little holes. The holes appear to have six sides. What type of polygon is Mustafa seeing?

In this concept, you will learn how to classify polygons.

Guidance

A polygon is a closed figure made up of lines and angles. A polygon is classified by its number of sides.

Here is a table with information on some of the different types of polygons.

Polygon Name Polygon Number of Angles and Sides Sum of Interior Angles
triangle 3 180\begin{align*}180^\circ\end{align*}
rectangle/square 4 360\begin{align*}360^\circ\end{align*}
pentagon 5 540\begin{align*}540^\circ\end{align*}
hexagon 6 720\begin{align*}720^\circ\end{align*}
heptagon 7 900\begin{align*}900^\circ\end{align*}
octagon 8 1,080\begin{align*}1,080^\circ\end{align*}
nonagon 9 1,260\begin{align*}1,260^\circ\end{align*}
decagon 10 1,440\begin{align*}1,440^\circ\end{align*}

Polygons have similar names. Look at the name for the shape that has eight angles and sides. It is called an octagon. In octagon, "oct" means “eight.” An octopus, for example, has eight arms. In pentagon, "pent" means “five,” so this is a shape with five sides.

Now take a look at the column on the right. Each kind of polygon has a different sum of its interior angles. For instance, the three angles in a triangle always add up to 180\begin{align*}180^\circ\end{align*}, and the four angles in a quadrilateral always add up to 360\begin{align*}360^\circ\end{align*}.

Let’s look at an example of classifying a polygon.

Identify the polygon below.

First, count the number of sides.

6 sides.

Then refer to the table.

The polygon is a hexagon.

Guided Practice

Identify the polygon below.

First, count the number of sides.

9 sides.

Then refer to the table.

The polygon is a nonagon.

Examples

Use what you have learned to identify each polygon.

Example 1

The sum of the interior angles is 180\begin{align*}180^\circ\end{align*}.

First, refer to the table to see the number of sides that correspond to the sum of the interior angles.

3 sides

Then, name the polygon.

Triangle

Example 2

It has seven sides.

First, note the number of sides.

7

Then, refer to the table.

The shape is a heptagon.

Example 3

It has five sides and five angles.

First, note the number of sides.

The shape has five sides.

Then refer to the table.

The shape is a pentagon.

Remember Mustafa and the beehives? He sees that the tiny holes appear to have six sides. What type of polygon is Mustafa seeing?

First, write the number of sides.

6 sides

Then refer to the table.

The polygon is a hexagon.

Explore More

Identify the polygons in the diagram. Then find the measures of the unknown angles.

1.

Answer true or false for each of the following questions.

2. A rhombus is always a square.

3. A parallelogram has opposite sides that are parallel.

4. A rectangle is a type of parallelogram.

5. Squares, rectangles and rhombi are parallelograms with four right angles.

6. A trapezoid has four right angles.

7. A trapezoid has one pair of parallel sides.

Determine whether or not each image is a polygon. If yes, write polygon, if no, write not a polygon.

8.

9.

10.

11.

12.

13.

14.

15. A square tile on a floor

Vocabulary Language: English

Concave

Concave

A concave polygon has at least one interior angle greater than 180 degrees. A common way to identify a concave polygon is to look for a "caved-in" side of the polygon.
Convex

Convex

A convex polygon contains no interior angles greater than 180 degrees.
Diagonal

Diagonal

A diagonal is a line segment in a polygon that connects nonconsecutive vertices
Exterior angles

Exterior angles

An exterior angle is the angle formed by one side of a polygon and the extension of the adjacent side.
Interior angles

Interior angles

Interior angles are the angles inside a figure.
Parallelogram

Parallelogram

A parallelogram is a quadrilateral with two pairs of parallel sides.
Polygon

Polygon

A polygon is a simple closed figure with at least three straight sides.

A quadrilateral is a closed figure with four sides and four vertices.
Rectangle

Rectangle

A rectangle is a quadrilateral with four right angles.
Regular Polygon

Regular Polygon

A regular polygon is a polygon with all sides the same length and all angles the same measure.
Rhombus

Rhombus

A rhombus is a quadrilateral with four congruent sides.
Square

Square

A square is a polygon with four congruent sides and four right angles.
Vertices

Vertices

Vertices are points where line segments intersect.
Equilateral

Equilateral

A polygon is equilateral if all of its sides are the same length.

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Date Created:
Dec 02, 2015