3-5+Properties+of+Parallel+Lines

3-5 Properties of Parallel Lines Matthew Saidel James Morriarty

__Summary__ This section will teach you how to prove two lines are parallel. Also it teaches you two new theorems about parallel and perpendicular lines. Lastly this chapter teaches you why lines are parallel. The first goal in this chapter is to use parallel lines in real life. The last goal is teaching you how to construct parallel lines.

__Helpful Websites__ [] []

Theorem 3.11 If two lines are parallel to the same line, then they are parallel to each other. Theorem 3.12 In a plane, if two lines are perpendicular to the same line, then they are parallel to each other. __Sample Problems__ Example 1 Lines //m//, //n//, and //k// represent three of the oars above. //m//   //n// and //n//    //k//. Prove that //m//   //k//.
 * from book**
 * From Book**
 * From Book**


 * SOLUTION**[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif width="100%" height="8"]]
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/given_arrow.gif align="absmiddle"]] || //m// [[image:http://images.classwell.com/ebooks/images/mcd_geo/parallel.gif align="absmiddle"]]  //n//, //n//  [[image:http://images.classwell.com/ebooks/images/mcd_geo/parallel.gif align="absmiddle"]]  //k// ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/prove_arrow.gif align="absmiddle"]] || //m// [[image:http://images.classwell.com/ebooks/images/mcd_geo/parallel.gif align="absmiddle"]]  //k// ||

Example 2 In the diagram below, each step is parallel to the step immediately below it and the bottom step is parallel to the floor. Explain why the top step is parallel to the floor.
 * From Book**



Example 3 You are building a CD rack. You cut the sides, bottom, and top so that each corner is composed of two 45° angles. Prove that the top and bottom front edges of the CD rack are parallel.
 * SOLUTION**[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif width="100%" height="8"]]
 * You are given that //k//1 [[image:http://images.classwell.com/ebooks/images/mcd_geo/parallel.gif align="absmiddle"]] //k//2 and //k//2 [[image:http://images.classwell.com/ebooks/images/mcd_geo/parallel.gif align="absmiddle"]] //k//3. By transitivity of parallel lines, //k//1 [[image:http://images.classwell.com/ebooks/images/mcd_geo/parallel.gif align="absmiddle"]] //k//3. Since //k//1 [[image:http://images.classwell.com/ebooks/images/mcd_geo/parallel.gif align="absmiddle"]] //k//3 and //k//3 [[image:http://images.classwell.com/ebooks/images/mcd_geo/parallel.gif align="absmiddle"]] //k//4, it follows that //k//1 [[image:http://images.classwell.com/ebooks/images/mcd_geo/parallel.gif align="absmiddle"]] //k//4. So, the top step is parallel to the floor. ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif width="100%" height="11"]] ||
 * From Book**



__Practice Review Problems__ //j//   //n//, //k//    //n//
 * SOLUTION**[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif width="100%" height="8"]]
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/given_arrow.gif align="absmiddle"]] || //m//[[image:http://images.classwell.com/ebooks/images/mcd_geo/angle.gif align="absmiddle"]] 1 = 45°, //m//[[image:http://images.classwell.com/ebooks/images/mcd_geo/angle.gif align="absmiddle"]] 2 = 45°[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif width="100%" height="8"]] //m//[[image:http://images.classwell.com/ebooks/images/mcd_geo/angle.gif align="absmiddle"]] 3 = 45°, //m//[[image:http://images.classwell.com/ebooks/images/mcd_geo/angle.gif align="absmiddle"]] 4 = 45°[[image:http://images.classwell.com/ebooks/images/mcd_geo/blank.gif width="100%" height="8"]] ||
 * [[image:http://images.classwell.com/ebooks/images/mcd_geo/prove_arrow.gif align="absmiddle"]] || [[image:http://images.classwell.com/ebooks/images/mcd_geo/linesegment_ba.gif align="absmiddle"]] [[image:http://images.classwell.com/ebooks/images/mcd_geo/parallel.gif align="absmiddle"]] [[image:http://images.classwell.com/ebooks/images/mcd_geo/linesegment_cd.gif align="absmiddle"]] ||
 * State the postulate or theorem that allows you to conclude that //j// [[image:http://images.classwell.com/ebooks/images/mcd_geo/parallel.gif align="absmiddle"]]  //k//.**

//j//   //n//, //k//    //n//


 * Explain how you would show that //k// [[image:http://images.classwell.com/ebooks/images/mcd_geo/parallel.gif align="absmiddle"]]  //j//. State any theorems or postulates that you would use.**