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Geometry
Polygons
A polygon is a flat, 2-dimensional figure made up
of 3 or more line segments called sides.
◆ The sides of a polygon are connected end to end and
make one closed path.
◆ The sides of a polygon do not cross.
Each endpoint where two sides meet is called a vertex.
The plural of vertex is vertices.
Figures That Are Polygons
4 sides, 4 vertices
3 sides, 3 vertices
7 sides, 7 vertices
Figures That Are NOT Polygons
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All sides of a polygon must
be line segments. Curved lines
are not line segments.
The sides of a polygon must
form a closed path.
A polygon must have
at least 3 sides.
The sides of a polygon
must not cross.
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Geometry
Polygons are named after the number of their sides.
The prefix for a name tells the number of sides.
Prefixes
triangle
quadrangle or
quadrilateral
pentagon
hexagon
heptagon
octagon
tri-
3
quad-
4
penta-
5
hexa-
6
hepta-
7
octa-
8
nona-
9
deca-
10
dodeca-
12
The flag of Nepal is the
only flag in the world with
5 sides. All other flags
have 4 sides. The flag of
Switzerland has a white
cross with an edge that is
a dodecagon (12 sides).
flag of Nepal
flag of
Switzerland
nonagon
1. Name the polygon.
a. 6 sides
b. 4 sides
d. 8 sides
e. 12 sides
c. 10 sides
2. Draw a pentagon whose sides are not all the same length.
Check your answers on page 339.
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Geometry
A regular polygon is a polygon whose sides
all have the same length and whose angles are
all the same size.
The hexagon shown here is a regular hexagon.
All six sides are the same length.
All six angles are the same size.
Some regular polygons have special names.
60°
60°
60°
A regular triangle is called an equilateral
triangle. It has 3 sides that are the same
length. It has 3 angles that each measure 60°.
90°
90°
90°
90°
A square is a regular quadrangle (quadrilateral).
It has 4 sides that are the same length. It has
4 angles that each measure 90°.
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A design using
equilateral triangles
Laying a square
tile floor
Geometry
The Pentagon in Washington, D.C. has a ground area of
1,263,240 square feet. It has a larger ground area than
any other office building in the world. The outside walls
of the Pentagon have the shape of a regular pentagon.
The inside walls of the Pentagon also have the shape of
a regular pentagon. The 5 angles of a regular pentagon
each measure 108°.
A stop sign has the shape
of a regular octagon. It has
8 sides that are the same
length. It has 8 angles that
each measure 135°.
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Geometry
Triangles
Triangles are the simplest type of polygon. The prefix
“tri-” means three. All triangles have 3 sides, 3 vertices,
and 3 angles.
Name the parts of the triangle below.
_ _
_
The sides are BC, BA, and CA. The sides are the line
segments that form the triangle.
The vertices are the points B, C, and A. Each endpoint
where two sides meet is called a vertex.
The angles are ∠ B, ∠C, and ∠ A. An angle is formed by
the two sides
_that meet
_ at a vertex. For example, ∠ B is
formed by BC and BA.
Triangles have 3-letter names. You name a triangle
by listing the letters for each vertex in order. The
triangle in the example above has 6 possible names:
triangle BCA, BAC, CAB, CBA, ABC, or ACB.
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Geometry
Triangles have many different sizes and shapes.
Two special types of triangles have been given names.
Equilateral Triangles
An equilateral triangle is a triangle with all 3 sides
the same length. All equilateral triangles have the
same shape.
Right Triangles
A right triangle is a triangle with 1 right angle
(square corner). Right triangles can have many
different shapes.
Other triangles are shown below. None of these is
an equilateral triangle. None is a right triangle.
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Geometry
Quadrangles
A quadrangle is a polygon that has
4 sides. Another name for quadrangle
is quadrilateral. The prefix “quad-”
means four. All quadrangles have 4 sides,
4 vertices, and 4 angles.
A quadricycle is a vehicle
similar to the bicycle and
tricycle but having 4 wheels.
Name the parts of the quadrangle.
_
The sides are RS, ST, TU, and UR.
The vertices are R, S, T, and U.
The angles are ∠R, ∠S, ∠T, and ∠U.
Some quadrangles have 2 pairs of parallel sides.
These quadrangles are called parallelograms.
Reminder
Two sides are parallel if they are parts
of lines that are parallel (never cross).
Figures That Are Parallelograms
Opposite sides are parallel in each figure.
Figures That Are NOT Parallelograms
no parallel sides
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only 1 pair of parallel sides
3 pairs of parallel sides,
but a parallelogram
must have 4 sides
Geometry
Some quadrangles have special names.
Some of them are parallelograms.
Others are not parallelograms.
Quadrangles That Are Parallelograms
Rectangles are parallelograms.
They have 4 right angles (square corners).
The sides of a rectangle do not all have to be
the same length.
Rhombuses are parallelograms.
Their 4 sides are all the same length.
Squares are parallelograms.
They have 4 right angles (square corners).
Their 4 sides are all the same length.
All squares are rectangles.
All squares are rhombuses.
Quadrangles That Are NOT Parallelograms
Trapezoids have exactly 1 pair of parallel sides.
Their 4 sides can all be different lengths.
Kites are 4-sided polygons with 2 pairs of equal sides.
The equal sides are next to each other.
Their 4 sides cannot all be the same length.
A rhombus is not a kite because all 4 sides of the
rhombus are the same length.
others Any polygon with 4 sides that is not a
parallelogram, a trapezoid, or a kite
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