Polygons

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Polygons

• 5.4

Pre-Algebra
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Warm Up
1. How many sides does a hexagon have? 2. How
many sides does a pentagon have? 3. How many
angles does an octagon have? 4. Evaluate (n
2)180 for n 7.
6
5
8
900
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Learn to classify and find angles in polygons.
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Vocabulary
polygon regular polygon trapezoid parallelogram re
ctangle rhombus square
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The cross section of a brilliant-cut diamond is a
pentagon. The most beautiful and valuable
diamonds have precisely cut angles that maximize
the amount of light they reflect.
A polygon is a closed plane figure formed by
three or more segments. A polygon is named by the
number of its sides.
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Number of Sides
Polygon
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Example Finding Sums of the Angle Measures in
Polygons
A. Find the sum of the angle measures in a
hexagon.
Divide the figure into triangles.
4 triangles
4 180 720
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Example Finding Sums of the Angle Measures in
Polygons Continued
B. Find the sum of the angle measures in a
octagon.
Divide the figure into triangles.
6 triangles
6 180 1080
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Try This
A. Find the sum of the angle measures in a
hexagon.
Divide the figure into triangles.
4 triangles
4 180 720
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Try This
B. Find the sum of the angle measures in a
heptagon.
Divide the figure into triangles.
5 triangles
5 180 900
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The pattern is that the number of triangles is
always 2 less than the number of sides. So an
n-gon can be divided into n 2 triangles. The
sum of the angle measures of any n-gon is 180(n
2). All the sides and angles of a regular
polygon have equal measures.
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Example Finding the Measure of Each Angle in a
Regular Polygon
Find the angle measures in the regular polygon.
6 congruent angles
6x 180(6 2)
6x 180(4)
6x 720
x 120
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Example Finding the Measure of Each Angle in a
Regular Polygon
Find the angle measures in the regular polygon.
4 congruent angles
4y 180(4 2)
4y 180(2)
4y 360
y 90
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Try This
Find the angle measures in the regular polygon.
5 congruent angles
5a 180(5 2)
a
5a 180(3)
a
a
5a 540
a
a
a 108
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Try This
Find the angle measures in the regular polygon.
8 congruent angles
8b 180(8 2)
8b 180(6)
8b 1080
b 135
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Example Classifying Quadrilaterals
Give all the names that apply to the figure.
quadrilateral
Four-sided polygon
parallelogram
2 pairs of parallel sides
rectangle
4 right angles
rhombus
4 congruent sides
square
4 congruent sides and 4 right angles
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Example Classifying Quadrilaterals Continued
Give all the names that apply to the figure.
quadrilateral
Four-sided polygon
parallelogram
2 pairs of parallel sides
rhombus
4 congruent sides
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Try This
Give all the names that apply to the figure.
A.
quadrilateral
Four-sided polygon
parallelogram
2 pairs of parallel sides
rectangle
4 right angles
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Try This
Give all the names that apply to the figure.
B.
quadrilateral
Four-sided polygon
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Lesson Quiz Part 1
1. Find the sum of the angle measures in a
quadrilateral. 2. Find the sum of the angle
measures in a hexagon. 3. Find the measure of
each angle in a regular octagon.
360
720
135
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Lesson Quiz Part 2
4. Write all of the names that apply to the
figure below.
quadrilateral, rhombus, parallelogram