Transcript Slide 1

7-4
Classifying Polygons
Warm Up
Problem of the Day
Lesson Presentation
Course 3
7-4 Classifying Polygons
Warm Up
1. How many sides does a hexagon have?
6
2. How many sides does a pentagon have?
5
3. How many angles does an octagon have?
8
4. Evaluate (n – 2)180 for n = 7.
900
Course 3
7-4 Classifying Polygons
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?
6
Course 3
7-4 Classifying Polygons
Learn to classify and find angles in
polygons.
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7-4 Insert
Lesson
Title Here
Classifying
Polygons
Vocabulary
polygon
regular polygon
trapezoid
parallelogram
rectangle
rhombus
square
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7-4 Classifying Polygons
A polygon is a closed plane figure
formed by three or more segments. A
polygon is named by the number of its
sides.
Course 3
7-4 Classifying Polygons
Polygon
Triangle
Quadrilateral
Pentagon
Hexagon
Heptagon
Octagon
n-gon
Course 3
Number of
Sides
3
4
5
6
7
8
n
7-4 Classifying Polygons
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°
Course 3
7-4 Classifying Polygons
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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7-4 Classifying Polygons
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°
Course 3
7-4 Classifying Polygons
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°
Course 3
7-4 Classifying Polygons
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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7-4 Classifying Polygons
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°
6x° = 720°
6
6
x° = 120°
Course 3
7-4 Classifying Polygons
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°
4y° = 360°
4
4
y° = 90°
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7-4 Classifying Polygons
Check It Out: Example 2A
Find the angle measures in the regular polygon.
5 congruent angles
5a° = 180°(5 – 2)
a°
a°
a°
5a° = 180°(3)
5a° = 540°
a°
a°
5a° = 540°
5
5
a° = 108°
Course 3
7-4 Classifying Polygons
Check It Out: Example 2B
Find the angle measures in the regular polygon.
8 congruent angles
b°
b°
b°
8b° = 180°(8 – 2)
b°
b°
b°
b°
b°
8b° = 180°(6)
8b° = 1080°
8b° 1080°
=
8
8
b° = 135°
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7-4 Classifying Polygons
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.
Course 3
7-4 Classifying Polygons
Course 3
7-4 Classifying Polygons
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
Course 3
7-4 Classifying Polygons
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
Course 3
7-4 Classifying Polygons
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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7-4 Classifying Polygons
Check It Out: Example 3B
Give all the names that apply to the figure.
quadrilateral
Four-sided polygon
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7-4 Insert
Classifying
Polygons
Lesson
Title Here
Lesson Quiz: Part I
1. Find the sum of the angle measures in a
quadrilateral. 360°
2. Find the sum of the angle measures in a
hexagon. 720°
3. Find the measure of each angle in a regular
octagon. 135°
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7-4 Insert
Classifying
Polygons
Lesson
Title Here
Lesson Quiz: Part II
4. Write all of the names that apply to the figure
below.
quadrilateral,
rhombus,
parallelogram
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