6.7 Regular Polygons - arrowheadschools.org Regular Poly… · Smartboard Notes 6.7.notebook 19...

Smartboard Notes 6.7.notebook

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October 15, 2018

Dec 13­3:08 PM

6.7 Regular Polygons

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October 15, 2018

Dec 13­3:13 PM

Recall, what is a polygon?A union of segments in the same plane such that each segment intersects two others, one at each of its endpoints

Smartboard Notes 6.7.notebook

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October 15, 2018

Dec 13­3:13 PM

Define Regular Polygon: A convex polygon which is EQUILATERAL and

EQUIANGULAR.

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October 15, 2018

Dec 13­3:14 PM

The two most "famous" regular polygons we’ve discussed so far are

SquareEquilateral Triangle

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October 15, 2018

Dec 13­3:17 PM

Other regular polygons that are being discussed are…(Give the number of sides, and the total angle measure)

PENTAGON

HEXAGON

HEPTAGON

180(5 ‐ 2) = 540

180(7 ‐ 2) = 900

180(6 ‐ 2) = 720

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October 15, 2018

Dec 13­3:19 PM

OCTAGON

NONAGON

DECAGON

180(8 ‐ 2) = 1080

180(9 ‐ 2)= 1260

180(10 ‐ 2)=1440

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October 15, 2018

Dec 13­3:22 PM

Define Equilateral and Equiangular Polygons:

If THE SIDES of a polygon have the same LENGTH

the polygon is EQUILATERAL. If THE ANGLES of a polygon have the same measure, then polygon is called EQUIANGULAR.

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October 15, 2018

Oct 19­5:57 PM

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October 15, 2018

Dec 13­3:25 PM

Define Center of Regular Polygon Theorem: In any regular polygon, there is a point (it’s CENTER)which is equidistant from all of its vertices.

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October 15, 2018

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0

180

10

170

20

160

30

150

40

140

50

130

60

120

70

110

80

100

90

90

48°

100

80

110

70

120

60

130

50

140

40

150

30

160

20

170

10

180

0

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October 15, 2018

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October 15, 2018

Dec 13­3:26 PM

Given: UOTCE is a regular polygon. Proof:

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October 15, 2018

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0°

160

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October 15, 2018

Dec 13­3:30 PM

Draw in the symmetry lines, if any, then draw the center of symmetry, if it exists. If it does, label it point C.

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October 15, 2018

Oct 12­2:08 PM

0°100

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October 15, 2018

Dec 13­3:31 PM

Find the magnitude of rotation/each interior angle of a polygon!

Since regular polygons have lines of symmetry, we can use those lines of symmetry, and the center point to find out the magnitude of rotation and the interior angle.

Using the figure at the right, draw the lines of symmetry and plot center point, C.

Connect all vertices to center point C.

The degree measure of a circle is_________.

Therefore 360/n = __________ = ___________for the magnitude of rotation/each interior angle.

Smartboard Notes 6.7.notebook

20

October 15, 2018

Dec 13­3:31 PM

Find the magnitude of rotation/each interior angle of a polygon!

Since regular polygons have lines of symmetry, we can use those lines of symmetry, and the center point to find out the magnitude of rotation and the interior angle.

Using the figure at the right, draw the lines of symmetry and plot center point, C.

Connect all vertices to center point C.

The degree measure of a circle is_________.

Therefore 360/n = __________ = ___________for the magnitude of rotation/each interior angle.

C

Smartboard Notes 6.7.notebook

21

October 15, 2018

Dec 13­3:31 PM

Find the magnitude of rotation/each interior angle of a polygon!

Since regular polygons have lines of symmetry, we can use those lines of symmetry, and the center point to find out the magnitude of rotation and the interior angle.

Using the figure at the right, draw the lines of symmetry and plot center point, C.

Connect all vertices to center point C.

The degree measure of a circle is_________.

Therefore 360/n = __________ = ___________for the magnitude of rotation/each interior angle.

C

360360/4 90O

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October 15, 2018

Dec 13­3:36 PM

360/5 = 72360/6 = 60360/7 = 51.4360/8 = 45

360/9 = 40

360/10 = 36

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October 15, 2018

Oct 14­9:09 PM

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October 15, 2018

Oct 25­8:46 AM

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October 15, 2018

Oct 25­12:20 PM

0°104

0

18010 17020 16030 15040 14050 13060 12070 11080 10090 903° 100 80110 70120 60130 50140 40150 30160 20170 10180 0

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October 15, 2018

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0°91

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