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

Polygon

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

PolygonPolygon 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

Polygons

Nonexamples

Types of PolygonsRegular or IrregularIf 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

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

PolygonsCan be concave or convex.

Concave Convex

Non-convex polygons have some diagonalsthat do not lie within the figure. Some interiorangles are reflex (greater than 180°).

The diagonals of the convexpolygon all lie within thefigure.

Polygons are named by number of sidesNumber of Sides Polygon

34

5

6

78

9

10

12

n

TriangleQuadrilateral

Pentagon

Hexagon

Heptagon

Octagon

Nonagon

Decagon

Dodecagon

n-gon

Sums of Interior Angles

Draw a: Quadrilateral Pentagon 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 tablePolygon # of sides # of triangles Sum of

interior angles

Sums of Interior Angles

Triangle Quadrilateral Pentagon

Heptagon OctagonHexagon

= 2 triangles = 3 triangles

= 4 triangles= 5 triangles = 6 triangles

Polygon # of sides

# of triangles

Sum of interior angles

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

n-gon

3

4

5

6

7

8

n

3

4

5

6

n - 2

2

1 180°

2 x 180 = 360°

3 x 180 = 540°

4 x 180 = 720°

5 x 180 = 900°

6 x 180 = 1080°

(n – 2) x 180°

Polygon # of sides

# of triangles

Sum of interior angles

Triangle

Quadrilateral

Pentagon

Hexagon

Heptagon

Octagon

n-gon

3

4

5

6

7

8

n

3

4

5

6

n - 2

2

1 180°

2 x 180 = 360°

3 x 180 = 540°

4 x 180 = 720°

5 x 180 = 900°

6 x 180 = 1080°

(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.SolutionAngle sum = (18 − 2) × 180°= 16 × 180°= 2880°

Find the angle sum of a polygon with sides.SolutionAngle sum = (4 − 2) × 180°= 2 × 180°= 360°.

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