Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
Warm Up
1. A ? is a three-sided polygon.
2. A ? is a four-sided polygon.
Evaluate each expression for n = 6.
3. (n – 4) 12
4. (n – 3) 90
Solve for a.
5. 12a + 4a + 9a = 100
triangle
quadrilateral
24
270
4
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Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
To find and use the measures of interior and exterior angles of polygons.
Learning Targets
7-1
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
side of a polygon
vertex of a polygon
diagonal
regular polygon
concave
convex
Vocabulary
7-1
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
A polygon is a closed plane figure formed by three or more segments.
What is a polygon?
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Holt McDougal 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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Holt McDougal Geometry
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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Holt McDougal Geometry
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, hexagonpolygon, heptagon
not a polygon
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Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
Check It Out! Polygon or Not Polygon?
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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Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
N.B.If a polygon is not regular, it is called irregular.
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Three Types of polygon:
Equilateral polygons – all sides are equal.
Regular polygons – both equilateral & equiangular.
Equiangular polygons – all angles are equal.
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
A polygon is concave – If it caves in, it is concave.
A polygon is convex – If it does not cave in, it is
convex.
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There are 2 shapes of regular polygons:
Holt McDougal Geometry
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
regular, convex
irregular, concave
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Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
Check It Out! Example 2a
Tell whether the polygon is regular or irregular. Tell whether it is concave or convex.
regular, convex
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Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
To find the sum of the interior angle measures of a convex polygon, draw
all possible diagonals from one vertex of the polygon. This creates a set
of triangles. The sum of the angle measures of all the triangles equals the
sum of the angle measures of the polygon.
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Holt McDougal Geometry
6-1 Properties and Attributes of Polygons7-1
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
The formula of the sum of the angle measures of all these triangles is (n — 2)180°.
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Holt McDougal Geometry
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 12-gon. n =12.
Step 1 Find the sum of the interior angle measures.
Step 2 Find the measure of one interior angle.
(12 – 2)180° = 1800°
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1800°/12 =150°
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
Finding Interior Angle Measures and Sums in
Polygons
7-1
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
Finding Interior Angle Measures and Sums in
Polygons
7-1
Try this one:
Find the sum of the interior angle measures of the
following convex polygons and one interior angle.
13 - gon, n=13
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
Finding Interior Angle Measures and Sums in
Polygons
7-1
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
Finding Interior Angle Measures and Sums in
Polygons
7-1
Try this one:
The sum of the measures of the interior angles
of a convex polygon is 1200 deg. Classify the
number of sides.
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
Finding Interior Angle Measures and Sums in
Polygons
7-1
Polygon Interior Angles Theorem
The sum of the measures of interior angles of a quadrilateral is 360 degrees.
Find the value of x.
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
Finding Interior Angle Measures and Sums in
Polygons
7-1
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
Exterior Angles of Polygon:
The sum of the exterior angle measures is 360°.
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Holt McDougal Geometry
6-1 Properties and Attributes of Polygons7-1
Holt McDougal 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.
The measure of each exterior angle of a regular 20-gon is 18°.
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Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
Example 4A: Finding Interior Angle Measures and
Sums in Polygons
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Holt McDougal Geometry
6-1 Properties and Attributes of Polygons
Check It Out! Example 4b
Find the value of r in polygon JKLM.
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Holt McDougal Geometry
6-1 Properties and Attributes of Polygons7-1
Try this one:
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons7-1
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons7-1
Class work 7-1: Due next class 1/11/2017 (B) and 1/12/2017 (A)Question # 3, 4, 7, 9, 11, 13, 15, 17, 19, 21
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons7-1
Class work 7-1: Due next class 1/11/2017 (B) and 1/12/2017 (A)Question # 3, 4, 7, 9, 11, 13, 15, 17, 19, 21
Holt McDougal Geometry
6-1 Properties and Attributes of Polygons7-1
Class work 7-1: Due next class 1/11/2017 (B) and 1/12/2017 (A)Question # 3, 4, 7, 9, 11, 13, 15, 17, 19, 21