+ sum of interior angles. + what is a polygon? a polygon is a flat shape with strait sides. polygons...

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Sum of Interior angles

+What is a polygon?

• A polygon is a flat shape with strait sides.

• Polygons have a minimum of three sides.

• Polygons have no maximum number of sides.

• Polygons that have three sides are called triangles.

• Polygons that have four sides are called quadrilaterals.

• An n-gon is a polygon with n sides.

+Convex? Concave?

Convex – all of the angles are less than 180º.

Concave – one or more interior angles are more than 180º.

+Regular or Irregular Polygon?

The sides of regular polygons are all equal.

The sides of an irregular polygon are different lengths.

These are both polygons

+What is an interior angle?

+What is a diagonal?

Diagonals connect non adjacent vertices of a polygon.

To draw a diagonal pick one point and draw a line to all the non adjacent vertices from that point.

+How do I find the sum of the interior angles of a convex polygon? 1. Identify the polygon (how many sides).

2. Draw the diagonals

3. Count the number of triangles

4. Times the number of triangles by 180º

5. Equals the sum of the interior angles of the polygon Make sure you use proper units!

Before we do a few examples let’s look at how to draw diagonals.

+Step 1: Identify the Polygon

Sqaure – 4 sides

+Step 2: Draw the DiagonalsStep 3: Count the Triangles

Number of Triangles = 2

+Step 4: Times the Number of Triangles by 180ºStep 5: Equals the sum of the interior angles of the polygon

2 * 180 = 360

Interior sum of angles of a square is 360º

Is this true? Tell me why you think this is true (or false)?

+Example 2

Name the polygon

+Example 2

Draw the diagonals

Count the triangles

3 * 180 = 540º

+Example 3

Identify the polygon

+Example 3

Draw the diagonals

Count the triangles

4 * 180 = 720º

+Now it’s your turn!

Pull out your Sum of Interior Angles table.

Work with your desk partner to complete the table and answer the questions following the chart.

Be on the lookout for patterns!

+Patterns

Is there a pattern to the table? What is it?

Can this pattern help you find a formula?

What is the formula? (n-2) * 180 = sum of interior angles

Example (8-2) * 180 = 1080 Does this match your table?

+Knowing the Angle

What if I already know the sum of interior angles. Can I tell what size the polygon is?

I solve for n!

Example (n-2) * 180 = 900 [(n-2) * 180]/180 = 900/180 n-2 = 5 (n-2) + 2 = 5 + 2 n = 7

Answer: 7-gon or Heptagon

+Important Things to Remember

The definition of a polygon

The difference between a convex and concave polygon

The difference between a regular polygon and an irregular polygon

How to find the sum of interior angles using the triangles method and using the formula

The names of polygons with 3 sides through 10 sides (triangle, quadrilateral, pentagon, etc). All polygons larger 11 or larger may be called 11-gon.

Remember your units!