3. Paralleland PerpendicularLines................................................................................................
Linesand Angles
LearningObjectives
- Identifyparallellines,skewlines,and parallelplanes.
- Knowthe statementof and use the ParallelLine Postulate.
- Knowthe statementof and use the PerpendicularLine Postulate.
- Identifyanglesmadeby transversals.
Introduction
In this chapter, you will explorethe differenttypesof relationshipsformedwith paralleland perpendicular
linesand planes.Thereare manydifferentwaysto understandthe anglesformed,and a numberof tricks
to find missingvaluesand measurements.Thoughthe conceptsof paralleland perpendicularlinesmight
seemcomplicated,they are presentin our everydaylife. Roadsare oftenparallelor perpendicular, as are
crucialelementsin construction,suchas the wallsof a room.Rememberthat everytheoremand postulate
in this chaptercan be usefulin practicalapplications.
Paralleland PerpendicularLinesand Planes,and SkewLines
Parallellines are two or morelines that lie in the sameplaneand neverintersect.
We use the symbol for parallel,so to describethe figureabovewe wouldwrite. Whenwe
drawa pair of parallellines,we use an arrowmark to showthat the linesare parallel.Just like with
congruentsegments,if thereare two (or more)pairsof parallellines,we use one arrow for one pair
and two (or more)arrows for the otherpair.
Perpendicularlinesintersectat a right angle.Theyform a angle.This intersectionis usuallyshown
by a smallsquarebox in the angle.