6001 sum of angles polygons
TRANSCRIPT
![Page 1: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/1.jpg)
Geometry Drill 1/24/13 Pick up a paper and use your
protractor to find the sum of the interior angles of the polygons that have a check next them.
Write down the sum and the number of sides
![Page 2: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/2.jpg)
Geometry Drill 1/24/13 1. What is the sum of the
angles of a triangle? 2. What is the sum of the
angles of a square?
![Page 3: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/3.jpg)
Objective:
To determine the interior and exterior angle sum in any polygon.
To determine the measure of one interior & one exterior angle of a regular polygon.
![Page 4: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/4.jpg)
POLYGON......1.A CLOSED PLANE FIGURE
2. EACH SEGMENT INTERSECTS EXACTLY TWO OTHER SEGMENTS ONE AT EACH ENDPOINT.
3. MADE OF 3 OR MORE SEGMENTS
![Page 5: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/5.jpg)
WHICH ARE POLYGONS?
![Page 6: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/6.jpg)
Convex or Concave Polygons ?
![Page 7: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/7.jpg)
Convex Polygons
![Page 8: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/8.jpg)
CONVEX POLYGONA polygon in which any line
segment connecting two points has no part outside the polygon.
![Page 9: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/9.jpg)
CONVEX POLYGON.
![Page 10: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/10.jpg)
Sides Interior Angle Sum
3 180
4 360
5 540
6 720
7 900
8 1080
9 1260
10 1440
n
![Page 11: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/11.jpg)
Conjecture/Formula The sum of the measures of the angles of a convex polygon with n sides is _ .
![Page 12: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/12.jpg)
Conjecture/Formula The sum of the measures of the angles of a convex polygon with n sides is 180(n–2) _ .
![Page 13: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/13.jpg)
How many exterior angles are in the drawing?
CD
E
![Page 14: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/14.jpg)
exterior angles
E
D C
![Page 15: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/15.jpg)
10 exterior angles
E
D C
![Page 16: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/16.jpg)
We will only be interested in ONE AT A VERTEX
E
D C
![Page 17: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/17.jpg)
Conjecture/ Formula The sum of the measures
of the exterior angles of any convex polygon, one at each vertex is _____.
![Page 18: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/18.jpg)
Conjecture/ Formula The sum of the measures
of the exterior angles of any convex polygon, one at each vertex is 360º.
![Page 19: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/19.jpg)
Regular Polygon
A polygon with all sides and angles congruent.
![Page 20: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/20.jpg)
Conjecture/Formula The measure of one interior
angle of any regular convex polygon is _____.
![Page 21: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/21.jpg)
Conjecture/Formula The measure of one interior
angle of any regular convex polygon is
180(n–2)
n
![Page 22: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/22.jpg)
Conjecture/Formula The measure of one
exterior angle of any regular convex polygon is _____.
![Page 23: 6001 sum of angles polygons](https://reader035.vdocuments.us/reader035/viewer/2022062313/558b4c9fd8b42a2d2a8b4732/html5/thumbnails/23.jpg)
Conjecture/Formula The measure of one
exterior angle of any regular convex polygon is 360º
n