6.1 polygons what is a polygon? a plane figure that meets these 2 conditions: –it is formed by...
TRANSCRIPT
![Page 1: 6.1 Polygons What is a polygon? A plane figure that meets these 2 conditions: –it is formed by three or more segments called sides (no 2 sides with a](https://reader035.vdocuments.us/reader035/viewer/2022072006/56649f435503460f94c63e04/html5/thumbnails/1.jpg)
6.1 Polygons
![Page 2: 6.1 Polygons What is a polygon? A plane figure that meets these 2 conditions: –it is formed by three or more segments called sides (no 2 sides with a](https://reader035.vdocuments.us/reader035/viewer/2022072006/56649f435503460f94c63e04/html5/thumbnails/2.jpg)
What is a polygon?
• A plane figure that meets these 2 conditions:– it is formed by three or more
segments called sides (no 2 sides with a common endpoint are collinear)
- Each side intersects exactly 2 other sides, one at each endpoint.
![Page 3: 6.1 Polygons What is a polygon? A plane figure that meets these 2 conditions: –it is formed by three or more segments called sides (no 2 sides with a](https://reader035.vdocuments.us/reader035/viewer/2022072006/56649f435503460f94c63e04/html5/thumbnails/3.jpg)
Example of a Polygon
vertex
side
vertexB
A
E
D
C
![Page 4: 6.1 Polygons What is a polygon? A plane figure that meets these 2 conditions: –it is formed by three or more segments called sides (no 2 sides with a](https://reader035.vdocuments.us/reader035/viewer/2022072006/56649f435503460f94c63e04/html5/thumbnails/4.jpg)
Identifying polygons
I J
KL
![Page 5: 6.1 Polygons What is a polygon? A plane figure that meets these 2 conditions: –it is formed by three or more segments called sides (no 2 sides with a](https://reader035.vdocuments.us/reader035/viewer/2022072006/56649f435503460f94c63e04/html5/thumbnails/5.jpg)
Not PolygonsB
A
E
C
F
I J
KL
![Page 6: 6.1 Polygons What is a polygon? A plane figure that meets these 2 conditions: –it is formed by three or more segments called sides (no 2 sides with a](https://reader035.vdocuments.us/reader035/viewer/2022072006/56649f435503460f94c63e04/html5/thumbnails/6.jpg)
Naming Polygons
vertex
side
vertexB
A
E
D
C
Name a polygon by listing its vertices consecutively
CDEAB or ABCDE
![Page 7: 6.1 Polygons What is a polygon? A plane figure that meets these 2 conditions: –it is formed by three or more segments called sides (no 2 sides with a](https://reader035.vdocuments.us/reader035/viewer/2022072006/56649f435503460f94c63e04/html5/thumbnails/7.jpg)
More on naming…
• Polygons are named by the number of sides they have.
![Page 8: 6.1 Polygons What is a polygon? A plane figure that meets these 2 conditions: –it is formed by three or more segments called sides (no 2 sides with a](https://reader035.vdocuments.us/reader035/viewer/2022072006/56649f435503460f94c63e04/html5/thumbnails/8.jpg)
Convex vs. Concave
• A polygon is convex if no line containing a side of the polygon does not contain a
point in the interior of the polygon.
![Page 9: 6.1 Polygons What is a polygon? A plane figure that meets these 2 conditions: –it is formed by three or more segments called sides (no 2 sides with a](https://reader035.vdocuments.us/reader035/viewer/2022072006/56649f435503460f94c63e04/html5/thumbnails/9.jpg)
Concave
A polygon is concave if when a side is extended, it contains points in the interior of the polygon.
![Page 10: 6.1 Polygons What is a polygon? A plane figure that meets these 2 conditions: –it is formed by three or more segments called sides (no 2 sides with a](https://reader035.vdocuments.us/reader035/viewer/2022072006/56649f435503460f94c63e04/html5/thumbnails/10.jpg)
Convex or Concave??
![Page 11: 6.1 Polygons What is a polygon? A plane figure that meets these 2 conditions: –it is formed by three or more segments called sides (no 2 sides with a](https://reader035.vdocuments.us/reader035/viewer/2022072006/56649f435503460f94c63e04/html5/thumbnails/11.jpg)
Regular Polygons
• A polygon is regular if it is equilateral (all sides are congruent) and equiangular (all interior angles are congruent).
![Page 12: 6.1 Polygons What is a polygon? A plane figure that meets these 2 conditions: –it is formed by three or more segments called sides (no 2 sides with a](https://reader035.vdocuments.us/reader035/viewer/2022072006/56649f435503460f94c63e04/html5/thumbnails/12.jpg)
Diagonals
• Diagonals of a polygon are segments that join 2 nonconsecutive vertices.
![Page 13: 6.1 Polygons What is a polygon? A plane figure that meets these 2 conditions: –it is formed by three or more segments called sides (no 2 sides with a](https://reader035.vdocuments.us/reader035/viewer/2022072006/56649f435503460f94c63e04/html5/thumbnails/13.jpg)
Interior angles of a quadrilateral…
Add to 360º
![Page 14: 6.1 Polygons What is a polygon? A plane figure that meets these 2 conditions: –it is formed by three or more segments called sides (no 2 sides with a](https://reader035.vdocuments.us/reader035/viewer/2022072006/56649f435503460f94c63e04/html5/thumbnails/14.jpg)
Find angle Q and angle R
70
x2x
80
P
QR
S •80+70+x+2x=360
•150+3x=360
•3x=210
•X = 70
•Angle Q =70
•AngleR is 2(70)=140