PreAP Geometry

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Pre-AP Geometry

• Unit 1
• Points, Lines, Planes, and Angles

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Objectives

• 1.1 .1 Use the term equidistant.
• 1.1.2 Use the terms point and line.
• 1.1.3 Draw representations of points and lines.
• 1.2.1 Use the undefined terms point, line, and
  plane.
• 1.2.2 Draw representations of points, lines, and
  planes.
• 1.2.3 Use the terms collinear, coplanar, and
  intersection.
• 1.3.1 Use symbols for lines, segments, rays, and
  distances.
• 1.3.2 Find distances.
• 1.3.3 State and use the Ruler Postulate and the
  Segment Addition Postulate.
• 1.4.1 Name angles and find their measure.
• 1.4.2 State and use the Angle Addition Postulate.
• 1.4.3 Recognize what can be concluded from a
  diagram.
• 1.5.1 Use postulates and theorems relating
  points, lines, and planes.

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Introduction to Geometry
Geometry (Greek ?e?µet??a geo earth, metria
measure) is a part of mathematics concerned with
questions of size, shape, and relative
position of figures and with properties of space.
Geometry is one of the oldest sciences.
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Introduction to Geometry

• Geometry is a type of math used to measure
  things that are impossible to measure with
  devices.
• For example, no one has been able take a tape
  measure around the earth, yet we are pretty
  confident that the circumference of the planet at
  the equator is 24,901.473 miles.
• The first known case of calculating the
  distance around the earth was done by
  Eratosthenes around 240 BC.

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Introduction to Geometry

• The study of Geometry includes proofs.
• Proofs are not unique to Geometry. They could
  have been done in Algebra or delayed until
  Calculus.
• The reason that high school geometry almost
  always spends a lot of time with proofs is that
  the first great Geometry textbook,
• "The Elements," was written exclusively with
  proofs.

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Introduction to Geometry

• This course, for the most part, is based on
  Euclidean geometry.
• "Euclidean" (or "elementary") refers to the book
  "The Elements" written over 2,000 years ago by a
  man named Euclid.

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Introduction to Geometry

• Euclid started with some basic concepts.
• He built upon those concepts to create more and
  more concepts.
• His structure and method influence the way that
  geometry is taught today.

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Introduction to Geometry

• This course will include more than just facts
  about geometric objects the ability to "prove"
  that a particular answer is correct using logic
  and reason is the most important part of this
  course.

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Basic Figures

• Point
• A point is a geometric element that has position
  but no dimensions and is used to define an exact
  location in space.
• A point has no volume, area, or length, making it
  a zero dimensional object.
• A point is defined by its coordinates.

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Basic Figures

• Line
• A line can be described as an ideal zero-width,
  infinitely long, perfectly straight curve (the
  term curve in mathematics includes "straight
  curves") containing an infinite number of points.
  
• In Euclidean geometry, exactly one line can be
  found that passes through any two points.

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Basic Figures

• Equidistant - equally distant from any two or
  more points.

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Basic Figures

• Suppose that you and a friend are partners in a
  game in which you must locate various clues to
  win. You are told to pick up your next clue at a
  point that
• Is as far from the fountain as from the oak tree
• and
• 2. Is 10 m from the telephone pole.
• You locate X, which satisfies both requirements,
  but grumble because there simply isnt any clue
  to
• be found at X.
• Is there another location that
  satisfies both requirements?

10m
X
Equal distances
Discussion in GSP
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Review Quiz

• Which language does the word geometry come from
  and what does it mean?
• What is the circumference of the Earth at the
  equator? (exact value is preferred, but the
  nearest 1000 is acceptable)
• Who wrote the book The Elements?
• Which geometric element has dimensions of zero?
• How many points does it take to define a line?

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Problem Set 1.1, p. 3 1 - 10
Challenge Question 1 What is the speed that
the Earth rotates on its axis at the
equator? Challenge Question 2 What is the
speed that the Earth revolves around the
sun? State any facts and/or assumptions that you
use. Show your calculations in a logical and
sequential order.