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6-1 Properties and Attributes of Polygons
Warm Up
1. A
?
2. A
?
is a three-sided polygon. triangle
is a four-sided polygon. quadrilateral
Evaluate each expression for n = 6.
3. (n – 4) 12
24
4. (n – 3) 90
270
Solve for a.
5. 12a + 4a + 9a = 100 4
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6-1 Properties and Attributes of Polygons
6-1 Properties and Attributes of Polygons
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Geometry
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Geometry
6-1 Properties and Attributes of Polygons
Each 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.
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6-1 Properties and Attributes of Polygons
You can name a polygon
by the number of its
sides. The table shows
the names of some
common polygons.
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6-1 Properties and Attributes of Polygons
Example 1A: Identifying Polygons
Tell whether the figure is a polygon. If it is a
polygon, name it by the number of sides.
polygon, hexagon
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6-1 Properties and Attributes of Polygons
Example 1B: Identifying Polygons
Tell whether the figure is a polygon. If it is a
polygon, name it by the number of sides.
polygon, heptagon
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6-1 Properties and Attributes of Polygons
Example 1C: Identifying Polygons
Tell whether the figure is a polygon. If it is a
polygon, name it by the number of sides.
not a polygon
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6-1 Properties and Attributes of Polygons
Check It Out! Example 1a
Tell whether each figure is a polygon. If it is a
polygon, name it by the number of its sides.
not a polygon
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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.
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6-1 Properties and Attributes of Polygons
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. A regular polygon is always
convex.
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6-1 Properties and Attributes of Polygons
Example 2A: Classifying Polygons
Tell whether the polygon is regular or
irregular. Tell whether it is concave or convex.
irregular, convex
Holt Geometry
6-1 Properties and Attributes of Polygons
Example 2B: Classifying Polygons
Tell whether the polygon is regular or
irregular. Tell whether it is concave or convex.
irregular, concave
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6-1 Properties and Attributes of Polygons
Check It Out! Example 2b
Tell whether the polygon is regular or irregular.
Tell whether it is concave or convex.
irregular, concave
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6-1 Properties and Attributes of Polygons
Holt Geometry
6-1 Properties and Attributes of Polygons
Example 3A: Finding Interior Angle Measures and
Sums in Polygons
Find the sum of the interior angle measures of a
convex heptagon.
(n – 2)180°
Polygon  Sum Thm.
(7 – 2)180°
A heptagon has 7 sides,
so substitute 7 for n.
900°
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Simplify.
6-1 Properties and Attributes of Polygons
Example 3B: Finding Interior Angle Measures and
Sums in Polygons
Find the measure of each interior angle of a
regular 16-gon.
Step 1 Find the sum of the interior angle measures.
(n – 2)180°
Polygon  Sum Thm.
(16 – 2)180° = 2520°
Substitute 16 for n
and simplify.
Step 2 Find the measure of one interior angle.
The int. s are , so divide by 16.
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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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6-1 Properties and Attributes of Polygons
Holt Geometry
6-1 Properties and Attributes of Polygons
Example 4A: Finding Interior Angle Measures and
Sums in Polygons
Find the measure of each exterior angle of a
regular 20-gon.
A 20-gon has 20 sides and 20 vertices.
sum of ext. s = 360°.
measure of one ext.  =
Polygon  Sum Thm.
A regular 20-gon
has 20  ext. s, so
divide the sum by
20.
The measure of each exterior angle of a regular
20-gon is 18°.
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6-1 Properties and Attributes of Polygons
Check It Out! Example 4b
Find the value of r in polygon JKLM.
Polygon
Ext.  Sum Thm.
4r° + 7r° + 5r° + 8r° = 360
°
24r = 360
r = 15
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Combine like terms.
Divide both sides by 24.
6-1 Properties and Attributes of Polygons
Example 5: Art Application
Ann is making paper stars for
party decorations. What is the
measure of 1?
1 is an exterior angle of a regular
pentagon. By the Polygon Exterior
Angle Sum Theorem, the sum of the
exterior angles measures is 360°.
A regular pentagon has 5 
ext. , so divide the sum by 5.
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6-1 Properties and Attributes of Polygons
Lesson Quiz
1. Name the polygon by the number
of its sides. Then tell whether the
polygon is regular or irregular,
concave or convex.
nonagon; irregular; concave
2. Find the sum of the interior angle
measures of a convex 11-gon.
1620°
3. Find the measure of each interior angle of a
regular 18-gon. 160°
4. Find the measure of each exterior angle of a
regular 15-gon. 24°
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6-1 Properties and Attributes of Polygons
Warm-Up(Pass back Papers!!!!!!!!!!!!!!!)
1. Name the polygon by the number
of its sides. Then tell whether the
polygon is regular or irregular,
concave or convex.
nonagon; irregular; concave
2. Find the sum of the interior angle
measures of a convex 11-gon.
1620°
3. Find the measure of each interior angle of a
regular 18-gon. 160°
4. Find the measure of each exterior angle of a
regular 15-gon. 24°
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