6.7 regular polygons - arrowheadschools.org regular poly… · smartboard notes 6.7.notebook 19...
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Dec 133:08 PM
6.7 Regular Polygons
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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
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Define Regular Polygon: A convex polygon which is EQUILATERAL and
EQUIANGULAR.
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The two most "famous" regular polygons we’ve discussed so far are
SquareEquilateral Triangle
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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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OCTAGON
NONAGON
DECAGON
180(8 ‐ 2) = 1080
180(9 ‐ 2)= 1260
180(10 ‐ 2)=1440
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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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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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0
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90
48°
100
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0
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Given: UOTCE is a regular polygon. Proof:
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0°
160
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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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0°100
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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.
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October 15, 2018
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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
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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.
C
360360/4 90O
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360/5 = 72360/6 = 60360/7 = 51.4360/8 = 45
360/9 = 40
360/10 = 36
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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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0°91
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