3-5+Properties+of+Parallel+Lines

=**Prove two lines are Parallel**=

Theorems of Parallel lines
Lines can be proved parallel by finding another line that they are both parallel and perpendicular to.

- If two lines are parallel to the same line, then the two lines are parallel to each other.
Example(words): If line a is parallel to line b, and line c is parallel to line b, than line a is parallel to line c Example(symbols): a||b - c||b - a||c

Theorem 3.12
- On a coordinate plane, if two lines are perpendicular to the same line, then the two lines are parallel to each other. Example(words): If line a is perpendicular to line b, and line c is perpendicular to line b, than line a is parallel to line c Example(symbols): a_|_b - b_|_c - a||c Sample Questions(use the diagram below for questions 1 and 2): 1. What is the relationship between linesb and c, how do you know? 2. If you knew that line b and c were parallel, and that lines a and b were perpendicular, could you find out if lines a and c are perpendicular? 3. If the two sides of Doug's swimming pool are parallel to his fence, are they parallel to each other? Sample Answers: 1. Lines b and c are parallel, using theorem 3.12, you can see that if line b is perpendicular to line a, and line c is perpendicular to line a, than line b and c are parallel. 2. Yes, using the Theorem 3.12, you can find out that line c is perpendicular to line a 3. Yes using Theorem 3.11 if two lines are parallel to another line, than they are parallel to each other. Because of this, you can prove that Doug's swimming pools sides are parallel to each other. Learn more at - http://www.clickandclimb.com/content/mathcontent/geometry/parallel-and-perpendicular-linesphp:// - library.thinkquest.org/C006354/5_2.html