# Learning intentions: What is a polygon? Sum of interior angles in polygons . - PowerPoint PPT Presentation

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Polygon. Learning intentions: What is a polygon? Sum of interior angles in polygons . How can I find angle measures in polygons without using a protractor?. Polygon. Polygon comes from Greek. . Poly- means "many" . gon means "angle". . Many angles. What is a polygon?

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Learning intentions: What is a polygon? Sum of interior angles in polygons .

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#### Presentation Transcript

Polygon

Learning intentions:

What is a polygon?

Sum of interior angles in polygons.

• How can I find angle measures in polygons without using a protractor?

Polygon

Polygon comes from Greek.

Poly- means "many"

gon means "angle".

Many angles

What is a polygon?

A polygon is a Plane shape with straight sides.

Polygons are 2-dimensional shapes. They are made of straight lines, and the shape is "closed" (all the lines connect up).

Resource:

http://www.mathsisfun.com/geometry/polygons.html

### Nonexamples

http://www.mathsisfun.com/geometry/polygons.html

Types of Polygons

Regular or Irregular

If all angles are equal and all sides are equal, then it is regular, otherwise it is irregular

Concave or Convex

A convex polygon has no angles pointing inwards. More precisely, no internal angle can be more than 180°.

If any internal angle is greater than 180° then the polygon is concave. (Think: concave has a "cave" in it)

Convex

Concave

### Polygons

• Can be concave or convex.

Concave Convex

The diagonals of the convex

polygonall lie within the

figure.

Non-convex polygons have some diagonals

that do not lie within the figure. Some interior

angles are reflex (greater than 180°).

### Polygons are named by number of sides

Triangle

3

4

Pentagon

5

Hexagon

6

Heptagon

7

8

Octagon

9

Nonagon

10

Decagon

12

Dodecagon

n

n-gon

Sums of Interior Angles

• Draw a:

 Hexagon  Heptagon

 Octogon

• Then draw diagonals to create triangles.

• A diagonal is a segment connecting two nonadjacent vertices (don’t let segments cross)

• Add up the angles in all of the triangles in the figure to determine the sum of the angles in the polygon.

• Complete this table

### Sums of Interior Angles

Triangle

Pentagon

= 2 triangles

= 3 triangles

Hexagon

Octagon

Heptagon

= 4 triangles

= 5 triangles

= 6 triangles

3

1

180°

4

2

2 x 180 = 360°

5

3

3 x 180 = 540°

4

4 x 180 = 720°

6

7

5

5 x 180 = 900°

8

6

6 x 180 = 1080°

n

n - 2

(n – 2) x 180°

3

1

180°

4

2

2 x 180 = 360°

5

3

3 x 180 = 540°

4

4 x 180 = 720°

6

7

5

5 x 180 = 900°

8

6

6 x 180 = 1080°

n

n - 2

(n – 2) x 180°

The angle sum of a polygon with n sides is given by:

angle sum = (n − 2) × 180° or 180(n − 2)°

Find the angle sum of a polygon with 18 sides.

Solution

Angle sum = (18 − 2) × 180°

= 16 × 180°

= 2880°

Find the angle sum of a polygon with sides.

Solution

Angle sum = (4− 2) × 180°

= 2× 180°

= 360°.

End