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Section 9.2
Polygons
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What You Will Learn
Polygons
Similar Figures
Congruent Figures
9.2-2
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Polygons
A polygon is a closed figure in a plane
determined by three or more straight
line segments.
9.2-3
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Polygons
The straight line segments that form the
polygon are called its sides, and a point
where two sides meet is called a vertex
(plural, vertices).
The union of the sides of a polygon and
its interior is called a polygonal region.
A regular polygon is one whose sides
are all the same length and whose
interior angles all have the same
measure.
9.2-4
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Polygons
Polygons are named according to
their number of sides.
9.2-5
Number
of Sides
Name
Number of
Sides
Name
3
Triangle
8
Octagon
4
Quadrilateral
9
Nonagon
5
Pentagon
10
Decagon
6
Hexagon
12
Dodecagon
7
Heptagon
20
Icosagon
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Polygons
Sides Triangles Sum of the Measures of
the Interior Angles
3
1
1(180º) = 180º
4
2
2(180º) = 360º
5
3
3(180º) = 540º
6
4
4(180º) = 720º
The sum of the measures of the
interior angles of an n-sided polygon
is (n – 2)180º.
9.2-6
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Types of Triangles
Acute Triangle
All angles are acute.
9.2-7
Obtuse Triangle
One angle is obtuse.
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Types of Triangles (continued)
Right Triangle
One angle is a right
angle.
9.2-8
Isosceles Triangle
Two equal sides.
Two equal angles.
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Types of Triangles (continued)
Equilateral Triangle
Three equal sides.
Three equal angles,
60º each.
9.2-9
Scalene Triangle
No two sides are
equal in length.
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Similar Figures
Two figures are similar if their
corresponding angles have the same
measure and the lengths of their
corresponding sides are in proportion.
9
6
4
4
3
9.2-10
6
6
4.5
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Example 3: Using Similar Triangles
to Find the Height of a Tree
Monique Currie plans to remove a tree
from her backyard. She needs to know
the height of the tree. Monique is 6 ft
tall and determines that when her
shadow is 9 ft long, the shadow of the
tree is 45 ft long (see Figure). How tall
is the tree?
9.2-11
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Example 3: Using Similar Triangles
to Find the Height of a Tree
9.2-12
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Example 3: Using Similar Triangles
to Find the Height of a Tree
Solution
Let x represent the height of the tree
height of tree
length of tree's shadow

height of Monique length of Monique's shadow
x 45

6
9
9x  270
x  30
The tree is 30 ft tall.
9.2-13
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Congruent Figures
If corresponding sides of two similar figures
are the same length, the figures are
congruent.
Corresponding angles of congruent figures
have the same measure.
9.2-14
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Quadrilaterals
Quadrilaterals are four-sided polygons, the
sum of whose interior angles is 360º.
Quadrilaterals may be classified according to
their characteristics.
9.2-15
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Quadrilaterals
Trapezoid
Parallelogram
Two sides are parallel.
9.2-16
Both pairs of opposite
sides are parallel. Both
pairs of opposite sides
are equal in length.
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Quadrilaterals
Rhombus
Rectangle
Both pairs of opposite
sides are parallel. The
four sides are equal in
length.
9.2-17
Both pairs of opposite
sides are parallel. Both
pairs of opposite sides
are equal in length. The
angles are right angles.
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Quadrilaterals
Square
Both pairs of opposite
sides are parallel. The
four sides are equal in
length. The angles are
right angles.
9.2-18
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Example 5: Angles of a Trapezoid
Trapezoid ABCD is shown.
a) Determine the measure of the
interior angle, x.
b) Determine the measure of the
exterior angle, y.
9.2-19
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Example 5: Angles of a Trapezoid
Solution
a) Determine the
measure of the
interior angle, x.
mRDAB  mRABC  mRABC  mRx  360
130  90  90  mRx  360
310  mRx  360
mRx  50
9.2-20
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Example 5: Angles of a Trapezoid
Solution
b) Determine the
measure of the
exterior angle, y.
mRx  mRy  180
mRy  180  mRx
mRy  180  50
mRy  130
9.2-21
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