Holt Geometry 6-1 Properties and Attributes of Polygons 6.1 Classify polygons based on their sides...
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Holt Geometry 6-1 Properties and Attributes of Polygons 6.1 Classify polygons based on their sides and angles. Find and use the measures of interior and exterior angles of polygons. Side of a polygon Vertex of a polygon Diagonal Regular polygon Concave convex Polygon Angle Sum Theorem Polygon Exterior Angle Sum Theorem
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Transcript of Holt Geometry 6-1 Properties and Attributes of Polygons 6.1 Classify polygons based on their sides...
Holt Geometry
6-1 Properties and Attributes of Polygons
6.1
Classify polygons based on their sides and angles.
Find and use the measures of interior and exterior angles of polygons.
Side of a polygonVertex of a polygonDiagonalRegular polygonConcaveconvex
Polygon Angle Sum TheoremPolygon Exterior Angle Sum Theorem
1.2.3.4.5.6.
Number your paper
Holt Geometry
6-1 Properties and Attributes of Polygons
Classifying polygons by number of sides.
Holt Geometry
6-1 Properties and Attributes of Polygons
A regular polygon is one that is both equilateral and equiangular.
If a polygon is not regular, it is called irregular.
Concave: any diagonal passes outside of the polygon
Convex:no diagonal passes outside the polygon
regular irregular
1.2.3.4.5.
Number your paper
Holt Geometry
6-1 Properties and Attributes of Polygons
Tell whether each polygon is regular or irregular and concave or convex.
1.
2.
3.
4.
5.
Draw these!
Holt Geometry
6-1 Properties and Attributes of Polygons
Examples: Sketch a polygon that meets each of the following characteristics, if possible.
1. convex, irregular hexagon
2. concave triangle.
3. Regular quadrilateral
4. convex nonagon
5. concave, regular pentagon
Holt Geometry
6-1 Properties and Attributes of Polygons
Find the sum of the interior angle measures of each convex polygon by drawing all possible diagonals from one vertex of the polygon.
How does the triangle sum theorem help you?
Holt Geometry
6-1 Properties and Attributes of Polygons
Holt Geometry
6-1 Properties and Attributes of Polygons
Example 1:
Find the sum of the interior angle measures of a convex heptagon.
Holt Geometry
6-1 Properties and Attributes of Polygons
Example 2:
Find the measure of each interior angle of pentagon ABCDE.
Holt Geometry
6-1 Properties and Attributes of Polygons
How would you calculate the measure of each interior angle of a regular decagon?
What if it’s not regular?
Interior Angles Exterior Angles
Sum of all angles
Measure of one if the polygon is REGULAR!
)2(180 n
n
n )2(180
Handbook page 19
Holt Geometry
6-1 Properties and Attributes of Polygons
What is the measure of each interior angle of a regular decagon?
What is the measure of each exterior angle of a regular decagon?
What is the SUM of all of the exterior angles?
Holt Geometry
6-1 Properties and Attributes of Polygons
In the polygons below, an exterior angle has been measured at each vertex. Notice that in each case, the sum of the exterior angle measures is 360°.
Angle measures of a convex polygon with n sides
Interior Angles Exterior Angles
Sum of all angles
Measure of one if the polygon is REGULAR!
)2(180 n
n
n )2(180
360
n
360
Holt Geometry
6-1 Properties and Attributes of Polygons
Find the value of b in polygon FGHJKL.
Example 3:
Holt Geometry
6-1 Properties and Attributes of Polygons
Example 4
Find the measure of each exterior angle of a regular 20-gon.
Holt Geometry
6-1 Properties and Attributes of Polygons
Ann is making paper stars for party decorations. If the pentagon in the center of the star is regular, what is the measure of 1? 2?
2
