1. Math 132 Prof: Anthony Calise www.mrcalise.weebly.com CCBC Dundalk
Introductory Geometry
Prof: Anthony Calise
CCBC Dundalk
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

2. NCTM Standard: Geometry
In grades preK–2, all students should
recognize, name, build, draw, compare, and sort two- and three-dimensional shapes;
describe attributes and parts of two-and three-dimensional shapes;
investigate and predict the results of putting together and taking apart two- and three-dimensional shapes. (p. 96)
Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

3. NCTM Standard: Geometry
In grades 3–5 all students should
sort, build, draw, model, trace, measure, and construct, the capacity to visualize geometric relationships
learn to reason and to make, test, and justify conjectures
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4. NCTM Standard: Geometry
In grades 6–8, all students should
precisely describe, classify, and understand relationships among types of two- and three-dimensional objects using their defining properties;
use visual tools such as networks to represent and solve problems. (p. 240)
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5. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
11-1 Basic Notions
Linear Notions
Planar Notions
Other Planar Notions
Angles
Angle Measurement
Types of Angles
Perpendicular Lines
A Line Perpendicular to a Plane
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6. Undefined terms: points, lines, and planes
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7. Point

8. Notes(Vocab)
Points: have no size, often represented with dots, and named with a capital letter. C A B

9. inea
col

10. Collinear: points that are lying in the same line.
Non-Collinear: Not lying in the same line. A B C C A B

11. ine

12. Lines: have no thickness, and extend infinitely in two directions
Lines: have no thickness, and extend infinitely in two directions. Named with two points, or a cursive letter. l Y X

13. P
LANE

14. Planes: Extend infinitely in all directions
Planes: Extend infinitely in all directions. It is flat and has no thickness. There are two ways to name a plane.
To Name a plane you need 3 non-collinear points.
You can also use a capital cursive letter.

15. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Lines
A line has no thickness and it extends forever in two directions.
Given two points, there is one and only one line that connects these points.
If P and Q are any two points, we can create a number line on the line PQ such that there is one-to-one correspondence between the points on the line and real numbers.
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16. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Linear Notions
Collinear points
Line ℓ contains points A, B, and C.
Points A, B, and C belong to line ℓ.
Points A, B, and C are collinear.
Points A, B, and D are not collinear.
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17. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Linear Notions
Between
Point B is between points A and C on line ℓ.
Point D is not between points A and C.
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18. segmen

19. Segments: Are parts of lines, they have two endpoints, and are named by using the two endpoints.

20. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Linear Notions
AB or BA
Line segment
A subset of a line that contains two points of the line and all points between those two points.
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21. R A

22. Rays: is a “half-line”. It has one endpoint and extends infinitely in one direction.

23. Opposite
R A S

24. Opposite Rays: share the same endpoint and go in opposite directions.

25. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Linear Notions AB
Ray
A subset of the line AB that contains the endpoint A, the point B, all points between A and B, and all points C on the line such that B is between A and C.
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26. Coplanar: Points and lines that are in the same Plane.

27. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Planar Notions
Coplanar
Points D, E, and G are coplanar.
Points D, E, F, and G are not coplanar.
Lines DE, DF, and FE are coplanar.
Lines DE and EG are coplanar.
Lines DE and EG are intersecting lines; they intersect at point E.
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28. el
para

29. Parallel Lines: are lines that are in the same plane and do not intersect. (Same Direction)

30. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Planar Notions
Parallel lines
Line m is parallel to line n. They have no points in common.
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31. Skew Lines

32. Skew Lines: Lines that are in different planes
Skew Lines: Lines that are in different planes (Different Directions and do not intersect)

33. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.
Planar Notions
Skew lines
Lines GF and DE are skew lines. They do not intersect, and there is no plane that contains them.
Concurrent lines
Lines DE, EG, and EF are concurrent lines; they intersect at point E.
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34. Parallel Planes
Parallel Planes: Two planes that never intersect.

35. A C B I D E H F G

36. Examples

38. Examples

39. Homework #1: (Due 2/6)
Look through a magazine, newspaper, website, brochure, etc.. and cut out or label five examples of basic geometry vocabulary words in the real world.