1. Unit 1 Points, Lines, Planes, and Angles
Pre-AP Geometry
Unit 1
Points, Lines, Planes, and Angles

2. Objectives:
Use the term equidistant Use the terms point and line Draw representations of points and lines Use the undefined terms point, line, and plane Draw representations of points, lines, and planes Use the terms collinear, coplanar, and intersection Use symbols for lines, segments, rays, and distances Find distances State and use the Ruler Postulate and the Segment Addition Postulate Name angles and find their measure State and use the Angle Addition Postulate Recognize what can be concluded from a diagram Use postulates and theorems relating points, lines, and planes.

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8. Introduction to Geometry
(Greek γεωμετρία; 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.

9. 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, miles. The first known case of calculating the distance around the earth was done by Eratosthenes around 240 BC.

10. 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.

11. 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.

12. 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.

13. 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.

14. 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.

15. 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.

16. Basic Figures
Equidistant - equally distant from any two or more points.

17. 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 isn’t any clue to
be found at X.
Is there another location that satisfies both requirements?
Basic Figures
10m X
Equal distances
Discussion in GSP

18. 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?

19. Problem Set 1.1, p. 3: #