6.7 Regular Polygons

Transcription

1 6.7 Regular Polygons Dec 13 3:08 PM 1

2 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 Dec 13 3:13 PM 2

3 Define Regular Polygon: A convex polygon which is EQUILATERAL and EQUIANGULAR. Dec 13 3:13 PM 3

4 The two most "famous" regular polygons we ve discussed so far are Equilateral Triangle Square Dec 13 3:14 PM 4

5 Other regular polygons that are being discussed are (Give the number of sides, and the total angle measure) PENTAGON 180(5 2) = 540 HEXAGON 180(6 2) = 720 HEPTAGON 180(7 2) = 900 Dec 13 3:17 PM 5

6 OCTAGON 180(8 2) = 1080 NONAGON 180(9 2)= 1260 DECAGON 180(10 2)=1440 Dec 13 3:19 PM 6

7 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. Dec 13 3:22 PM 7

8 Oct 19 5:57 PM 8

9 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. Dec 13 3:25 PM 9

10 Oct 19 5:59 PM 10

11 Oct 12 11:15 AM 11

12 Given: UOTCE is a regular polygon. Proof: Dec 13 3:26 PM 12

13 Dec 13 3:28 PM 13

14 Oct 19 6:00 PM 14

15 0 160 Oct 19 6:00 PM 15

16 Oct 24 1:30 PM 16

17 Draw in the symmetry lines, if any, then draw the center of symmetry, if it exists. If it does, label it point C. Dec 13 3:30 PM 17

18 100 0 Oct 12 2:08 PM 18

19 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. Dec 13 3:31 PM 19

20 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. C The degree measure of a circle is. Therefore 360/n = = for the magnitude of rotation/each interior angle. Dec 13 3:31 PM 20

21 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. 360 The degree measure of a circle is. 360/4 90 O Therefore 360/n = = for the magnitude of rotation/each interior angle. C Dec 13 3:31 PM 21

22 360/5 = /6 = /7 = /8 = /9 = /10 = 36 Dec 13 3:36 PM 22

23 Oct 14 9:09 PM 23

24 Oct 25 8:46 AM 24

25 Oct 25 12:20 PM 25

26 Oct 25 12:21 PM 26

27 Oct 25 12:21 PM 27

28 Oct 25 12:22 PM 28

29 Oct 26 1:14 PM 29

30 91 0 Oct 27 11:05 PM 30

31 Oct 27 11:06 PM 31

32 Oct 27 11:07 PM 32

33 Oct 19 6:05 PM 33

34 Oct 15 7:55 AM 34

35 Oct 27 11:08 PM 35

36 Oct 27 11:08 PM 36

37 Oct 27 11:08 PM 37

38 Oct 27 11:09 PM 38

39 Oct 27 11:11 PM 39

40 Oct 29 1:31 PM 40