3-1+Lines+and+Angles

3-1 Lines and Angles Brandon Alvarado Eric Stigliano

__Summary__ In this section, you will learn how to classify different lines and angles. There are different types of lines, including parallel and perpendicular. There are also different types of angles, including corresponding angles, alternate exterior angles, alternate interior angles, and consecutive interior lines, that are made by a transversal. With these lines and angles classifications, there are also different postulates that can proved. These include parallel and perpendicular postulates. (Pages 129 to 134).

__Websites To Help Teach the Subject__ Classifying Lines (Powerpoint): www.kyrene.org/Staff/hstaudohar/.../7.4%20**classifying**%20**lines**.pdf

Classifying Angles: http://www.math.com/school/subject3/lessons/S3U1L5GL.html

__Vocabulary__ __Sides (Definitions Taken From the Textbook)__ Parallel Lines- Lines that are coplanar and do not intersect.

Perpendicular Lines- Lines that intersect at a 90 degree angle.

Skew Lines- Lines that do not intersect and are not coplanar.

Transversal- A line that intersects two or more coplanar lines at different points.

Corresponding Angles- Angles that occupy corresponding positions. Angles 2 and 6 and 1 and 7 are corresponding angles.

Alternate Exterior Angles- Angles that lie outside the two lines on opposite sides of the transversal. Angles 1 and 8 and 2 and 7 are alternate exterior angles.

Alternate Interior Angles- Angles that lie between the two lines on opposite sides of the transversal. Angles 3 and 6 and 4 and 5 are alternate interior angles.

Consecutive Interior Angles- Angles that lie between the two lines on the same side of the transversal. Angles 3 and 5 and 4 and 6 are consecutive interior angles.

__Sample Problems__

1. What are the corresponding angles in this diagram? Angles 1 and 5; Angles 2 and 6 2. Name all of the alternate exterior and alternate interior angles in this diagram. __ Alternate Exterior Angles: __ Angles 2 and 8; Angles 1 and 7 __Alternate Interior Angles:__ Angles 4 and 6; Angles 3 and 5 3. If angle 3 is 120 degrees, what is the measure of angle 6? What is the reason for this? Angle 6 would be 60 degrees. Since these angles are consecutive interior angles, they add up to 180 degrees. 180- 120= 60 degrees.

Sample Problems:

1. What are the alternate exterior and alternate interior angles in this diagram? 2. What are the corresponding angles in this diagram? 3. If angle 3 is 106 degrees, what is the measure of angle 5? 4. If angle 2 is 80 degrees, what is the measure of angle 7?

Picture from icoachmath.com http://www.icoachmath.com/math_dictionary/Parallel_Planes.html

1. What is a line that is parallel to line RS? 2. Is line WZ perpendicular to line SX? 3. Is line UT skew to line SX? 4. What is a line that is perpendicular to line UZ?