6.7 regular polygons - arrowheadschools.org regular poly… · smartboard notes 6.7.notebook 19...
TRANSCRIPT
Smartboard Notes 6.7.notebook
1
October 15, 2018
Dec 133:08 PM
6.7 Regular Polygons
Smartboard Notes 6.7.notebook
2
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
3
October 15, 2018
Dec 133:13 PM
Define Regular Polygon: A convex polygon which is EQUILATERAL and
EQUIANGULAR.
Smartboard Notes 6.7.notebook
4
October 15, 2018
Dec 133:14 PM
The two most "famous" regular polygons we’ve discussed so far are
SquareEquilateral Triangle
Smartboard Notes 6.7.notebook
5
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
Smartboard Notes 6.7.notebook
6
October 15, 2018
Dec 133:19 PM
OCTAGON
NONAGON
DECAGON
180(8 ‐ 2) = 1080
180(9 ‐ 2)= 1260
180(10 ‐ 2)=1440
Smartboard Notes 6.7.notebook
7
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.
Smartboard Notes 6.7.notebook
8
October 15, 2018
Oct 195:57 PM
Smartboard Notes 6.7.notebook
9
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.
Smartboard Notes 6.7.notebook
10
October 15, 2018
Oct 195:59 PM
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
Smartboard Notes 6.7.notebook
11
October 15, 2018
Oct 1211:15 AM
Smartboard Notes 6.7.notebook
12
October 15, 2018
Dec 133:26 PM
Given: UOTCE is a regular polygon. Proof:
Smartboard Notes 6.7.notebook
13
October 15, 2018
Dec 133:28 PM
Smartboard Notes 6.7.notebook
14
October 15, 2018
Oct 196:00 PM
Smartboard Notes 6.7.notebook
15
October 15, 2018
Oct 196:00 PM
0°
160
Smartboard Notes 6.7.notebook
16
October 15, 2018
Oct 241:30 PM
Smartboard Notes 6.7.notebook
17
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.
Smartboard Notes 6.7.notebook
18
October 15, 2018
Oct 122:08 PM
0°100
Smartboard Notes 6.7.notebook
19
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
Smartboard Notes 6.7.notebook
22
October 15, 2018
Dec 133:36 PM
360/5 = 72360/6 = 60360/7 = 51.4360/8 = 45
360/9 = 40
360/10 = 36
Smartboard Notes 6.7.notebook
23
October 15, 2018
Oct 149:09 PM
Smartboard Notes 6.7.notebook
24
October 15, 2018
Oct 258:46 AM
Smartboard Notes 6.7.notebook
25
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
Smartboard Notes 6.7.notebook
26
October 15, 2018
Oct 2512:21 PM
Smartboard Notes 6.7.notebook
27
October 15, 2018
Oct 2512:21 PM
Smartboard Notes 6.7.notebook
28
October 15, 2018
Oct 2512:22 PM
Smartboard Notes 6.7.notebook
29
October 15, 2018
Oct 261:14 PM
Smartboard Notes 6.7.notebook
30
October 15, 2018
Oct 2711:05 PM
0°91
Smartboard Notes 6.7.notebook
31
October 15, 2018
Oct 2711:06 PM
Smartboard Notes 6.7.notebook
32
October 15, 2018
Oct 2711:07 PM
Smartboard Notes 6.7.notebook
33
October 15, 2018
Oct 196:05 PM
Smartboard Notes 6.7.notebook
34
October 15, 2018
Oct 157:55 AM
Smartboard Notes 6.7.notebook
35
October 15, 2018
Oct 2711:08 PM
Smartboard Notes 6.7.notebook
36
October 15, 2018
Oct 2711:08 PM
Smartboard Notes 6.7.notebook
37
October 15, 2018
Oct 2711:08 PM
Smartboard Notes 6.7.notebook
38
October 15, 2018
Oct 2711:09 PM
Smartboard Notes 6.7.notebook
39
October 15, 2018
Oct 2711:11 PM
Smartboard Notes 6.7.notebook
40
October 15, 2018
Oct 291:31 PM