Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many...
-
Upload
camron-fletcher -
Category
Documents
-
view
219 -
download
4
Transcript of Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many...
![Page 1: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/1.jpg)
Warm-Up
• Draw an example of a(n)…– Quadrilateral– Pentagon– Octagon
• and list how many sides the figure has.
![Page 2: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/2.jpg)
Geometry 6-1
Properties and Attributes of Polygons
![Page 3: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/3.jpg)
Definition
• A polygon is a closed plane figure formed by three or more segments that intersect only at their endpoints.
Polygons Not Polygons
![Page 4: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/4.jpg)
Parts of a PolygonEach segment that forms a polygon is a side of the polygon. The common endpoint of two sides is a vertex of the polygon. A segment that connects any two nonconsecutive vertices is a diagonal.
![Page 5: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/5.jpg)
Names of Polygons
![Page 6: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/6.jpg)
Determine whether a figure is a polygon. If it is, name it by number of
sides
polygon, hexagon polygon, heptagon
![Page 7: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/7.jpg)
not a polygon polygon, nonagon
![Page 8: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/8.jpg)
Definitions• A regular polygon is one that is both
equilateral and equiangular. If a polygon is not regular, it is called irregular.
• A polygon is concave if any part of a diagonal contains points in the exterior of the polygon.
• If no diagonal contains points in the exterior, then the polygon is convex.
![Page 9: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/9.jpg)
Tell whether the follow polygons are regular/irregular and concave/convex.
irregular, convex regular, convex
![Page 10: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/10.jpg)
irregular, concave
regular, convex
![Page 11: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/11.jpg)
Finding the Sum of the Interior Angles of a Polygon
• Step 1: Draw all possible diagonals from one vertex to the other vertices.
• Step 2: Multiply the number of triangles by 180°.
(3) x 180° = 540°
![Page 12: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/12.jpg)
Finding the Sum of the Interior Angles of a Polygon
![Page 13: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/13.jpg)
Example
• Find the sum of the interior angles of a heptagon.
![Page 14: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/14.jpg)
Example
• Find the measure of each interior angle of a regular 16-gon.
![Page 15: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/15.jpg)
Example
• Find the value of c.
![Page 16: Warm-Up Draw an example of a(n)… – Quadrilateral – Pentagon – Octagon and list how many sides the figure has.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649f435503460f94c63e19/html5/thumbnails/16.jpg)
Measure of Exterior Angles
Example:Find the measure of each exterior angle of a regular hexagon.