Chapter 4 Section 1

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Chapter 4 Section 1

• TWO- AND THREE DIMENSIONAL GEOMETRY

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Geometry in Action

• One aspect of geometry is the ability to
  visualize spatial relationships.
• One field that uses spatial relationships is
  marketing.
• Marketing is the business of promoting sales
  through techniques like advertising and
  packaging.

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Geometry in Action

• As consumers, you are the target of marketing
  campaigns for products that are geared to sell to
  teenagers.
• A marketing campaign often uses advertisements.
  Print advertisements require that a
  three-dimensional object be displayed on a
  two-dimensional surface.

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Geometry in Action

• Another aspect of marketing is product's
  packaging.
• A three-dimensional package must be illustrated
  using two-dimensional geometry, so that it can be
  designed and built.

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Packaging Designers

• When packaging designers determine the shape and
  design of a product's package, they must consider
  how to display the product's name and marketing
  slogan on faces of a three-dimensional shape.

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Billboard Assemblers

• Billboard assemblers (page 165) are responsible
  for transferring an oversized advertisement onto
  outdoor canvases.
• Assemblers must measure and accurately place
  preprinted strips that show the product, logo and
  message to passersby.

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Geometry is all around you. What you know about
geometry influences how you understand the world
you see.

• 1. Look at an analog clock. Make a list of what
  you see on the face of the clock that defines or
  models geometry.
• 2. Look at the walls, floor and ceiling of a
  room. Make a list of what you see that defines or
  models geometry.
• 3. Look at a chalkboard (or whiteboard) and tools
  used to write on it. Name geometric figures
  modeled by these objects.

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Build Understanding

• People understand each other best if they speak
  the same language. The language of mathematics
  includes images, words and symbols.
• Geometry is built on three terms
• point
• line
• plane
• These terms exist without a concrete definition,
  and are represented by simple figures.

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Name the Figure
Point A
A

• A point is a location in space.
• Although a point has no dimension, it is usually
  represented by a dot.

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Name the Figure
B
C

• A line is a set of points that extends without
  end in opposite directions.
• Two points determine a line.
• Points on the same line are collinear points.

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Name the Figure
E
D

• A line segment is a part of a line that consists
  of two endpoints and all points between them.

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Name the Figure
G
F
FG (ray FG)

• A ray is a part of a line that has one endpoint
  and extends without end in one direction.

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Name the Figure
/ ABC (angle ABC) / CBA (angle CBA) / B or /1
A
B
1
C
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/ ABC (angle ABC) / CBA (angle CBA) / B or /1

• An angle is formed by two rays with a common
  endpoint.
• The endpoint is called the vertex of the angle.
• The rays are called the sides of the angle.

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Name the Figure
/ ABC (angle ABC) / CBA (angle CBA) / B or /1
A
B
1
C
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Name the Figure
M
Plane XYZ or plane M

• A plane is a flat surface that extends without
  end in all directions.
• It is determined by three non-collinear points.
• Points on the same plane are coplanar points.

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Collinear Points
g
Collinear points are points that lie on the same
line. Points A, B and C are collinear.
Points that do not lie on the same line are
called non-collinear points. Points A, B and D
are non-collinear.
h
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Coplanar Points
Coplanar points are points that lie in the same
plane.
J
Points that do not lie in the same plane are
called non-coplanar points.
H
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Angles

• An angle is measured in units called degrees ()
• On a protractor, one scale shows degree measures
  from 0 to 180in a clockwise direction.
• The other scale shows these degree measures in a
  counterclockwise direction.

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How to read an angle
Ray ED crosses the inside scale at 42
D
m/ DEF 42
E
F
Line up ray EF on 0 segment
Place vertex E at center.
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How to read an angle
Ray ED crosses the outside scale at 95
D
m/ FED 95
F
E
Line up ray FE on 0 segment
Place vertex E at center.
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How to draw / JKL 120
J
K
L
Draw a ray from point K through point L.
Place the center of the protractor on the vertex
K. Place the 0 line of the protractor on KL.
Locate 120 on the inside scale. Mark point J.
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How to draw / JKL 90
J
K
L
Draw a ray from point K through point L.
Place the center of the protractor on the vertex
K. Place the 0 line of the protractor on KL.
Locate 90 on the inside scale. Mark point J.
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How to draw / JKL 160
J
K
L
Draw a ray from point K through point L.
Place the center of the protractor on the vertex
K. Place the 0 line of the protractor on KL.
Locate 160 on the inside scale. Mark point J.
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How to draw / JKL 10
J
K
L
Draw a ray from point K through point L.
Place the center of the protractor on the vertex
K. Place the 0 line of the protractor on KL.
Locate 10 on the inside scale. Mark point J.