Polygons 2015 2

POLYGONS IIBY PN. NOOR HATIFA BT MASO’D

What is a Polygon????

Any ideas?

Write down what you think it is for #1.

A polygon is a closed plane figure with 3 or more sides (all straight lines, no curves).

Classifying Polygons by # of Sides

3 sided Polygon =

TriangleHint: Think “Tri”cycle, “tri”pod, “Tri”lateration (Tri means 3)


4 sided Polygon =

Quadrilateral

Hint: Think “Quad”rant, “Quad”ruple, “Quad” (AKA 4-Wheeler)


5 sided Polygon =

Pentagon

Hint: Think “Pent”athalon, or the government building “The Pentagon”


6 sided Polygon =

HexagonHint: Both “Hexagon” and “Six” have an ‘x’ in them


7 sided Polygon =

Heptagon

Hint: ???


8 sided Polygon =

Octagon

Hint: “oct”opus – 8 legs


9 sided Polygon =

Nonagon

Hint: “Non” is similar to “Nine”


10 sided Polygon =

Decagon

Hint: Think “Dec”ade (10 years

Classifying Polygons by # of Sides# of Sides Name

3 Triangle

4 Quadrilateral

5 Pentagon

6 Hexagon

7 Heptagon

8 Octagon

9 Nonagon

10 Decagon

11 Hendecagon

12 Dodecagon

Two Types of Polygons

Convex – all vertices point outward

Concave – at least one vertex points inward towards the center of the polygon (The side looks like it “caved” in)

Regular Polygons

A Regular Polygon is a polygon in which all sides are the same length.

Equilateral Triangle Square

Regular

Pentagon Regular

Hexagon

Review of Similar Triangles

• 2 Triangles are similar if they have the same shape (i.e. the same angle in the same positions)

Similar Polygons

The same is true of polygons. 2 polygons are similar if they have the same angles in the same

positions (i.e. same shape)

^ Similar Pentagons ^

Similar Trapezoids

Similar Rectangles

EQ: How do I find the measure of an interior & exterior angle of a polygon?

F

A B

C

DE

A VERTEX is the point of intersection of two sides

A segment whose endpoints are two

nonconsecutive vertices is called a

DIAGONAL.

CONSECUTIVE VERTICES are two endpoints of any side.

Sides that share a vertex are called CONSECUTIVE SIDES.

IMPORTANT TERMS

Let us find the connection between the number of sides, number of

diagonals and the number of triangles

of a polygon.

Polygons

QuadrilateralPentagon

180o

180o 180o 180o

180o

2 x 180o = 360o

3

4 sides5 sides

3 x 180o = 540o

Hexagon6 sides

180o 180o

180o180o

4 x 180o = 720o 4 Heptagon/Septagon7 sides

180o180o 180o

180o

180o

5 x 180o = 900o 5

2 1 diagonal

2 diagonals

3 diagonals 4 diagonals Polygons

RegularPolygon

No. of sides No. of diagonals

No. of Sum of the interior angles

Each interior angle

Triangle 3 0 1 1800 1800/3= 600

Polygons

RegularPolygon



Each interior angle

Triangle 3 0 1 1800 1800/3= 600

Quadrilateral 4 1 2 2 x1800

= 36003600/4= 900

Polygons

RegularPolygon



Each interior angle

Triangle 3 0 1 1800 1800/3= 600


= 36003600/4= 900

Pentagon 5 2 3 3 x1800

= 54005400/5= 1080

Polygons

RegularPolygon



Each interior angle

Triangle 3 0 1 1800 1800/3= 600


= 36003600/4= 900


= 54005400/5= 1080

Hexagon 6 3 4 4 x1800

= 72007200/6= 1200

Polygons

RegularPolygon



Each interior angle

Triangle 3 0 1 1800 1800/3= 600


= 36003600/4= 900


= 54005400/5= 1080

Hexagon 6 3 4 4 x1800

= 72007200/6= 1200

Heptagon 7 4 5 5 x1800

= 90009000/7= 128.30

Polygons

RegularPolygon



Each interior angle

Triangle 3 0 1 1800 1800/3= 600


= 36003600/4= 900


= 54005400/5= 1080

Hexagon 6 3 4 4 x1800

= 72007200/6= 1200


= 90009000/7= 128.30

“n” sided polygon n Association with no. of sides

Association with no. of sides

Association with no. of triangles

Association with sum of interior angles

Polygons

RegularPolygon



Each interior angle

Triangle 3 0 1 1800 1800/3= 600


= 36003600/4= 900


= 54005400/5= 1080

Hexagon 6 3 4 4 x1800

= 72007200/6= 1200


= 90009000/7= 128.30

“n” sided polygon n n - 3 n - 2 (n - 2) x1800 (n - 2) x1800 / n

Polygons

FormulaSum of interior

angles (n -2) x 1800

Septagon/Heptagon

Decagon Hendecagon

7 sides

10 sides 11 sides9 sides

Nonagon

Sum of Int. Angles 900o

Interior Angle 128.6o

Sum 1260o

I.A. 140oSum 1440o

I.A. 144oSum 1620o I.A. 147.3o

Calculate the Sum of Interior Angles and each interior

angle of each of these regular polygons.

1

2 43

Polygons

2 x 180o = 360o

360 – 245 = 115o

3 x 180o = 540o

540 – 395 = 145o

y117o

121o

100o125o

140o z

133o 137o

138o

138o

125o

105o

Find the unknown angles below.Diagrams not

drawn accurately.

75o

100o

70o

wx

115o110o

75o 95o

4 x 180o = 720o

720 – 603 = 117o

5 x 180o = 900o

900 – 776 = 124oPolygons

An exterior angle of a regular polygon is formed by extending one side of the polygon.

Angle CDY is an exterior angle to angle CDE

Exterior Angle + Interior Angle of a regular polygon =1800

DE Y

B

C

A

F

12

Polygons

1200

1200

1200

600 600

600

Polygons

1200

1200

1200

Polygons

1200

1200

1200

Polygons

3600

Polygons

600

600

600

600

600

600

Polygons

600

600

600

600

600

600

Polygons

1

2

34

5

6

600

600600

600

600 600

Polygons

1

2

34

5

6

600

600600

600

600 600

Polygons

1

2

34

5

6

3600

Polygons

900

900

900

900

Polygons

900

900

900

900

Polygons

900

900

900

900

Polygons

1

23

4

3600

Polygons

No matter what type of polygon we have, the sum of the exterior angles is ALWAYS equal to

360º.

Sum of exterior angles = 360º

Polygons

In a regular polygon with ‘n’ sides

Sum of interior angles = (n -2) x 1800

Exterior Angle + Interior Angle =1800

Each exterior angle = 3600/n

No. of sides = 3600/exterior angle

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Polygons 2015 2