3.1+Lines+&+Angles

**__3.1 Lines & Angles__** Laura Bilash (Working with Deandra Donato)

This section will teach how to identify relationships in spaces. It will include the relationships between parallel, perpendicular and skew lines, and parallel plans. In addition, it will teach how to identify angle relationships as well. The difference between corresponding, alternate exterior, alternate interior, consecutive interior, and consecutive exterior angles will be shown through visual examples. With angles, it mainly involves relationships between the angles within the transversal. Once the position of the line or angle are clearly distinguished, it will be easy to determine the line or angle relationships.


 * //__Vocabulary__//

Parallel Lines- **  2 lines are parallel if they do not intersect and they are coplanar 
 * Perpendicular Lines- ** Perpendicular lines meet to form four right angles
 * Skew Lines- ** Two lines are skew if they do not intersect and are NOT coplanar
 * Parallel Lines- ** Planes that do not intersect


 * Transversal- ** A line that intersects two or more coplanar lines at different points
 * Corresponding Angles- ** Two angles are corresponding if they occupy matching positions
 * Alternate Exterior Angles- ** Two angles are alternate exterior if they lie outside of the two lines on opposite sides of the transversal
 * <span style="font-family: Georgia,serif;">Alternate Interior Angles- **<span style="font-family: Georgia,serif;"> Two angles are alternate interior angles if they lie between two lines on opposite sides of the transversal
 * <span style="font-family: Georgia,serif;">Consecutive (Same-Side) Interior Angles- **<span style="font-family: Georgia,serif;"> Two angles are consecutive interior angles if they lie between two lines on the same side of the transversal
 * <span style="font-family: Georgia,serif;">Consecutive (Same-Side) Exterior Angles- **<span style="font-family: Georgia,serif;"> Two angles are consecutive exterior angles if they lie outside the two lines on the same side of the transversal

<span style="font-family: Georgia,serif;">


 * <span style="font-family: Georgia,serif;">//__Postulates__//

Postulate 13: Parallel Postulate <span style="font-family: Georgia,serif; font-weight: normal;">If there is a line and a point not on the line, then there is <span style="font-family: Georgia,serif; font-weight: normal;"> exactly one line through the point parallel to the given line. <span style="font-family: Georgia,serif;">

Postulate 14: Perpendicular Postulate <span style="font-family: Georgia,serif; font-weight: normal;">If there is a line and a point not on the line, then there is exactly one line through the point perpendicular to the given line. **<span style="font-family: Georgia,serif;">


 * (Textbook pg. 130)**

1. A. Find a pair of corresponding angles B. Find a pair of alternate exterior angles C. Find a pair of consecutive interior angles
 * <span style="font-family: Georgia,serif;">//__Sample Problems__//

(Textbook pg. 132)

**<span style="font-family: Georgia,serif;">**2.** **<span style="font-family: Georgia,serif;"> A. Name a line parallel to <span style="font-family: Georgia,serif; font-weight: normal;"> B. Name a line skew to **<span style="font-family: Georgia,serif;">


 * (Textbook pg. 132)**


 * <span style="font-family: Georgia,serif;">3. **<span style="font-family: Georgia,serif;">
 * A**. < 10 and < 12 are _?_ angles. **B.** < 9 and < 14 are _?_ angles.
 * C.** < 8 and < 12 are _?_ angles. **D.** < 11 and < 12 are _?_ angles.


 * (Textbook pg. 132)**

<span style="font-family: Georgia,serif;">** *ALL ANSWERS TO SAMPLE PROBLEMS ARE ON THE ANSWERS TO PRACTICE PROBLEMS PAGE* **

Transversals Additional Information Parallel Lines & Transversals
 * //<span style="color: #ff0000; font-family: Georgia,serif;">*Online Extra Help*

Online Practice Problems Identify Pairs of Lines & Angles <span style="font-family: Georgia,serif; font-style: normal;"> //**//<span style="font-family: Georgia,serif;">TO GET TO PRACTICE PROBLEMS: Click on @Home Tutor, then, Lesson 1: Identify Pairs of Lines & Angles, then, <span style="font-family: Georgia,serif; font-style: normal;"> Try the Exercises//