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

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.

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 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

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) Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

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 Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Undefined terms: points, lines, and planes Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Point

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

inea col

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

ine

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

P LANE

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.

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. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

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. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

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. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

segmen

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

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. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

R A

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

Opposite R A S

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

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. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Coplanar: Points and lines that are in the same Plane.

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. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

el para

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

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. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Skew Lines

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

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. Copyright © 2013, 2010, and 2007, Pearson Education, Inc.

Parallel Planes Parallel Planes: Two planes that never intersect.

A C B I D E H F G

Examples

Examples

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.