#### Transcript 4CH5L4

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5-4 Polygons
Polygons
Warm Up
Problem of the Day
Lesson Presentation
Pre-Algebra
Pre-Algebra
5-4 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
Pre-Algebra
5-4 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
Pre-Algebra
5-4 Polygons
Learn to classify and find angles in
polygons.
Pre-Algebra
5-4 Polygons
Vocabulary
polygon
regular polygon
trapezoid
parallelogram
rectangle
rhombus
square
Pre-Algebra
5-4 Polygons
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.
Pre-Algebra
5-4 Polygons
Polygon
Triangle
Pentagon
Hexagon
Heptagon
Octagon
n-gon
Pre-Algebra
Number of
Sides
3
4
5
6
7
8
n
5-4 Polygons
Additional Example 1A: 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°
Pre-Algebra
5-4 Polygons
Additional Example 1B: 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°
Pre-Algebra
5-4 Polygons
Try This: Example 1A
A. Find the sum of the
angle measures in a
hexagon.
Divide the figure into
triangles.
4 triangles
4 • 180° = 720°
Pre-Algebra
5-4 Polygons
Try This: Example 1B
B. Find the sum of the angle
measures in a heptagon.
Divide the figure into
triangles.
5 triangles
5 • 180° = 900°
Pre-Algebra
5-4 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.
Pre-Algebra
5-4 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°
Pre-Algebra
5-4 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°
Pre-Algebra
5-4 Polygons
Try This: 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°
Pre-Algebra
5-4 Polygons
Try This: 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°
Pre-Algebra
5-4 Polygons
Pre-Algebra
5-4 Polygons
Give all the names that apply to the figure.
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
Pre-Algebra
5-4 Polygons
Continued
Give all the names that apply to the figure.
Four-sided polygon
parallelogram
2 pairs of parallel sides
rhombus
4 congruent sides
Pre-Algebra
5-4 Polygons
Try This: Example 3A
Give all the names that apply to the figure.
A.
Pre-Algebra
Four-sided polygon
parallelogram
2 pairs of parallel sides
rectangle
4 right angles
5-4 Polygons
Try This: Example 3B
Give all the names that apply to the figure.
B.
Four-sided polygon
Pre-Algebra
5-4 Polygons
Lesson Quiz: Part 1
1. Find the sum of the angle measures in a
2. Find the sum of the angle measures in a
hexagon. 720°
3. Find the measure of each angle in a regular
octagon. 135°
Pre-Algebra
5-4 Polygons
Lesson Quiz: Part 2
4. Write all of the names that apply to the figure
below.