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6-1 Properties and Attributes of Polygons
6.1
Classify polygons based on their sides and Side of a polygon
angles.
Vertex of a polygon
Diagonal
Regular polygon
Find and use the measures
of interior and exterior angles of
Concave
polygons.
convex
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Polygon Angle Sum Theorem
Polygon Exterior Angle Sum
Theorem
1.
2.
3.
4.
5.
6.
6-1 Properties and Attributes of Polygons
Classifying polygons by number of sides.
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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.
regular
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irregular
Concave: any diagonal
passes outside of the
polygon
Convex:no diagonal
passes outside the
polygon
1.
2.
3.
4.
5.
6-1 Properties and Attributes of Polygons
Tell whether each polygon is regular or
irregular and concave or convex.
Holt Geometry
1.
2.
4.
3.
5.
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
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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?
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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.
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6-1 Properties and Attributes of Polygons
Example 2:
Find the measure of each interior angle of
pentagon ABCDE.
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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?
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Interior Angles
Sum of all angles
180( n  2)
Measure of one if
the polygon is
REGULAR!
180( n  2)
n
Exterior Angles
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?
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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°.
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Angle measures of a convex polygon with n sides
Interior Angles
Exterior Angles
Sum of all angles
180(n  2)
Measure of one if
the polygon is
REGULAR!
180(n  2)
n
360
360
n
6-1 Properties and Attributes of Polygons
Example 3:
Find the value of b in polygon FGHJKL.
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6-1 Properties and Attributes of Polygons
Example 4
Find the measure of each exterior angle of a
regular 20-gon.
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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
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