1. Basicsof Geometry..........................................................................................................................
Points,Lines,and Planes
LearningObjectives
- Understandthe undefinedtermspoint,line, andplane.
- Understanddefinedterms,includingspace,segment,and ray.
- Identifyand applybasicpostulatesof points,lines,and planes.
- Drawand labeltermsin a diagram.
Introduction
Welcometo the excitingworldof geometry!Aheadof you lie manyexcitingdiscoveriesthat will help you
learnmoreaboutthe world.Geometryis usedin manyareas—fromart to science.For example,geometry
playsa key role in construction,fashiondesign,architecture,and computergraphics.This coursefocuses
on the mainideasof geometrythat are the foundationof applicationsof geometryusedeverywhere.In this
chapter, you’llstudythe basicelementsof geometry. Lateryou will provethingsaboutgeometricshapes
usingthe vocabularyand ideasin this chapter—somakesure that you completelyunderstandeachof the
conceptspresentedhere beforemovingon.
UndefinedTerms
The threebasicbuildingblocksof geometryarepoints,lines, andplanes. Theseare undefinedterms.
Whilewe cannotdefinethesetermsprecisely, we can get an idea of whatthey are by lookingat examples
and models.
Apointis a locationthat has no size. To imaginea point,look at the periodat the end of this sentence.Now
imaginethat periodgettingsmallerand smalleruntil it disappears.A pointdescribesa location,suchas the
locationof the period,but a pointhas no size.We use dots (like periods)to representpoints,but sincethe
dots themselvesoccupyspace,thesedots are not points—weonly use dots as representations.Pointsare
labeledwith a capitalletter, as shownbelow.
Alineis an infiniteseriesof pointsin a row. A line doesnot occupyspace,so to imaginea line you can
imaginethe thinneststringyou can thinkof, and shrinkit until it occupiesno spaceat all. A line has direction
and location,but still doesnot take up space.Linesare sometimesreferredto by one italicizedletter, but
they can also be identifiedby two pointsthat are on the line. Linesare calledone-dimensional,sincethey
havedirectionin one dimension.