Designed by Dave Meyer. All rights reserved Tutorial 5a.

Designed by Dave Meyer. All rights reserved

Tutorial 5aTutorial 5a


PolygonPolygon -- A union of segments -- A union of segments that meet only at endpoints.that meet only at endpoints.PolygonPolygon -- A union of segments -- A union of segments that meet only at endpoints.that meet only at endpoints.

1.


The following are The following are notnot Polygons. . .Polygons. . .


a)

b)

because a polygon consists entirely of segments.

because in a polygon only consecutive sides intersect and only at endpoints

A

B C

D

EF

2.




2.

c)

d)

cont...

P

R

O

NS

D

L Q

T

because each vertex must belong to exactly 2 sides (vertex P belongs to 3).

because each segment must meet exactly two other segments.


Parts of PolygonsParts of PolygonsParts of PolygonsParts of Polygons

• polygon ABCDEF• Vertices: A, B,

C, D, E, F

F

A

B C

D

E

3.




C, D, E, F

F

A

B C

D

E

• Sides: AB, BC, CD . . .

3.



F

A

B C

D

E


3.


C, D, E, F



F

A

B C

D

E


3.


C, D, E, F



F

A

B C

D

E


3.


C, D, E, F



F

A

B C

D

E


Diagonal -- A segment joining 2 nonadjacent vertices.

3.


C, D, E, F



F

A

B C

D

E


• Diagonals AC, BE, CF . . .

3.


C, D, E, F



F

A

B C

D

E



3.


C, D, E, F



F

A

B C

D

E



3.


C, D, E, F

Types of PolygonsTypes of PolygonsTypes of PolygonsTypes of Polygons

A polygon is convex if no diagonal contains points outside the polygon.

A polygon is concave if a diagonal contains points outside the polygon.

A

E

D

Y

T

D F

H

M

N

Q

4.


Convex polygon Convex polygon -- A polygon where all -- A polygon where all of its diagonals fall on the inside of the of its diagonals fall on the inside of the figure.figure.

Convex polygon Convex polygon -- A polygon where all -- A polygon where all of its diagonals fall on the inside of the of its diagonals fall on the inside of the figure.figure.

Which polygon is convex?Click on your choice.

A B

C

DE

Q R

S

TU

V

4. cont...


Regular Polygon Regular Polygon -- A convex polygon -- A convex polygon with all of its sides congruent and all with all of its sides congruent and all angles congruent.angles congruent.

Regular Polygon Regular Polygon -- A convex polygon -- A convex polygon with all of its sides congruent and all with all of its sides congruent and all angles congruent.angles congruent.

Q R

S

TU

V

4. cont...


Names of PolygonsNames of PolygonsNames of PolygonsNames of Polygons

triangle

quadrilateral

pentagon

hexagon

heptagon

octagon

nonagon

decagon

dodecagon

icosagon

Number of sides Name3

4

5

6

7

8

9

10

12

20

5.


Finding the sum of the angles of a polygonFinding the sum of the angles of a polygonFinding the sum of the angles of a polygonFinding the sum of the angles of a polygon

(n - 2)180

(5 - 2)180 =

(3)180 = 540

The sum of the measures of the interior angles of a polygon is (n - 2)180. Where n represents the number of sides.

The sum of all 5 angles in this polygon is 540º

6.


ApplicationsApplicationsApplicationsApplications

Find the sum of the interior angles of a:

pentagon

decagon

quadrilateral

6.(n - 2)180

Click the button below to check your answers!

cont...




pentagon

decagon

quadrilateral

540º

1440º

360º

6.(n - 2)180

Click on the answer to see the problem worked out!

cont...


If a polygon has angles with a sum of 720If a polygon has angles with a sum of 720º then how many sides does the polygon have?then how many sides does the polygon have?If a polygon has angles with a sum of 720If a polygon has angles with a sum of 720º then how many sides does the polygon have?then how many sides does the polygon have?

(n - 2)180 = 720180n - 360 = 720

180n = 1080

n = 6The polygon has 6 sides!

7.



How many sides does a polygon have if the sum of the measures of its interior angles is:720?

1440?

2700?

(n-2)180 = 720 ; n = 6 sides

(n-2)180 = 1440; n = 10 sides

(n-2)180 = 2700; n = 17 sides

7.(n - 2)180

cont...


More ApplicationsMore ApplicationsMore ApplicationsMore Applications

(n - 2)180

(6 - 2)180 = 720

720 - 700 = 20

7.

If the sum of the first five interior angles of a hexagon is 700, find the measure of the sixth angle.

cont...

The six angle measures 20º


Regular Polygon:Regular Polygon: A polygon that A polygon that is both equiangular and equilateralis both equiangular and equilateralRegular Polygon:Regular Polygon: A polygon that A polygon that is both equiangular and equilateralis both equiangular and equilateral

What’s the formula to find the measure of each angle of a regular polygonregular polygon?

(n - 2)180

n

8.



(n - 2)180

n

8.

Find the measure of each interior angle of a regular hexagon

cont...

(6 - 2)180

6

= 720

6

= 120º

120º



(n - 2)180

n

8. Each interior angle of a regular polygon

measures 135. Find the number of sides that the polygon has.

cont...

= 135

(n - 2)180 = 135n

180n - 360 = 135n

- 360 = - 45n 8 = n


Exterior AnglesExterior AnglesExterior AnglesExterior Angles9.

1

2

34

5

6

The The sum of the exterior angles of a polygon of a polygon is 360

Each exterior angle of a

regular polygon is 360

n


SummarySummarySummarySummary

The sum of the interior angles of a polygon is (n - 2)180

Each angle of a regular polygon measures (n - 2)180

n The sum of exterior angles is 360 Each exterior angle of a regular polygon is

360 n


Time to move on to the Time to move on to the assignment or the next lesson.assignment or the next lesson.

Time to move on to the Time to move on to the assignment or the next lesson.assignment or the next lesson.




pentagon A pentagon has 5 sides; So-

(n – 2)180 =

(5 – 2)180 =

(3)180 = 540º

6.(n - 2)180

cont...

Back




decagon A decagon has 10 sides; So-

(n – 2)180 =

(10 – 2)180=

(7)180 = 1440º

6.(n - 2)180

cont...

Back




quadrilateral A quadrilateral has 4 sides; So-

(n – 2)180 =

(4 – 2)180 =

(2)180 = 360º

6.(n - 2)180

cont...

Back

Designed by Dave Meyer. All rights reserved Tutorial 5a.

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