Classifying Polygons

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7-4
Classifying Polygons
M8A1.b Simplify and evaluate algebraic
expressions.
Warm Up
Problem of the Day
Lesson Presentation
CW/HW Assignments
Course 3
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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.
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5
8
900
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Problem of the Day Jeffrey planted four
carnations, three dahlias, seven marigolds, five
cornflowers, one geranium, and four mums. He
forgot to water them and on each of the two
following days, half the remaining flowers died.
How many flowers were still living at the end of
the second day?
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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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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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Additional Example 1A Finding Sums of the Angle
Measures in Polygons
Find the sum of the angle measures in a hexagon.
Divide the figure into triangles.
4 triangles
4 180 720
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Additional Example 1B Finding Sums of the Angle
Measures in Polygons Continued
Find the sum of the angle measures in a octagon.
Divide the figure into triangles.
6 triangles
6 180 1080
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Check It Out Example 1A
Find the sum of the angle measures in a hexagon.
Divide the figure into triangles.
4 triangles
4 180 720
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Check It Out Example 1B
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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Additional Example 2A 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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Additional Example 2B 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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Check It Out Example 2A
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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Check It Out Example 2B
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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Quadrilaterals with certain properties are given
additional names. A trapezoid has exactly 1 pair
of parallel sides. A parallelogram has 2 pairs of
parallel sides. A rectangle has 4 right angles. A
rhombus has 4 congruent sides. A square has 4
congruent sides and 4 right angles.
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Additional Example 3A 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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Additional Example 3B Classifying Quadrilaterals
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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Check It Out Example 3A
Give all the names that apply to the figure.
quadrilateral
Four-sided polygon
parallelogram
2 pairs of parallel sides
rectangle
4 right angles
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Check It Out Example 3B
Give all the names that apply to the figure.
quadrilateral
Four-sided polygon
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Lesson Quiz Part I
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 II
4. Write all of the names that apply to the
figure below.
quadrilateral, rhombus, parallelogram
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Assignments
1. Class Work Guided Practice problems 1-9
(all), pages 343-344. 2. Homework Problems 10-34
(even), pages 344-345.