Transcript Classifying Polygons (9-3)

Warm-Up for Lesson 9-3
Find ALL of the missing angle measures.
40°
60°
180-(40+60) = 80°
80°
60°
100° 80°
80° 100°
40
°
60° 120°
120° 60°
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Warm-Up for Lesson 9-3
s || t and c || d.
s
Name all the angles that are congruent to
1. Give a reason for each answer.
1
5
3  1
corresponding angles
6  1
vertical angles
8  1
alternate exterior angles
9  1
corresponding angles
14  1
alternate exterior angles
1  11
corresponding angles
1  16
alternate exterior angles
9
10
13 14
t
3
2
6
7
11
15
c
4
8
12
16
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d
Classifying Polygons (9-3)
How can you
classify a
triangle by the
lengths of its
sides?
How can you
classify a
triangle by the
measures of its
angles?
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Classifying Polygons (9-3)
How can you
classify a
quadrilateral by
its sides and
angles?
quadrilateral –
a four-sided
shape
par allelogram
– two pairs of
parallel sides
trapezoid – one
pair of parallel
sides
rhombus – four
congruent
(equal) sides
kite – two pairs of
congruent sides
that are adjacent
(next to one
another)
rectangle –
four right
angles
square – four right
angles and four
congruent sides
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Classifying Polygons (9-3)
What is a
regular
polygon?
regular polygon – a polygon (many-sided shape) in which all sides
and angles are congruent (equal).
Examples:
To find the sum of
the interior angles,
we divide the polygon
into triangles. For
example, there are
three triangles in a
pentagon, and
because the sum of
each triangle is 180°,
we get 540°, so the
measure of the interior
angles of a regular
pentagon is 540° and
each angle is 540° / 5,
or 108°. . There are
four triangles in a
hexagon, 180° x 4 =
720°, so the measure
of the interior angles of
a regular pentagon is
720° and each angle
is 720° / 6, or 120°.
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Classifying Polygons
LESSON 9-3
Additional Examples
Classify the triangle by its sides and angles.
The triangle has no congruent sides and one obtuse angle.
The triangle is a scalene obtuse triangle.
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Classifying Polygons
LESSON 9-3
Additional Examples
Name the types of quadrilaterals that have at least
one pair of parallel sides.
All parallelograms and trapezoids have at least one pair of parallel
sides.
Parallelograms include rectangles, rhombuses, and squares.
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Classifying Polygons
LESSON 9-3
Additional Examples
A contractor is framing the wooden deck shown below in the
shape of a regular dodecagon (12 sides). Write a formula to find the
perimeter of the deck. Evaluate the formula for a side length of 3 ft.
To write a formula, let x = the length of each side.
The perimeter of the regular dodecagon is
x + x + x + x + x + x + x + x + x + x + x + x.
Therefore a formula for the perimeter is P = 12x.
P = 12x
= 12(3)
Write the formula.
Substitute 3 for x.
= 36
Simplify.
For a side length of 3 ft, the perimeter is 36 ft.
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