A correctresponseis a diagramshowing:
-.
•.
•
.
If , , and are collinearand , , and are not collinearthen the conditionsare satisfied.
Diagrams
LearningObjectives
- Providethe diagramthat goeswith a problemor proof.
- Interpreta givendiagram.
- Recognizewhatcan be assumedfrom a diagramand whatcan not be.
- Use standardmarksfor segmentsand anglesin diagrams.
Introduction
Geometryis aboutobjectssuchas points,lines,segments,rays,planes,and angles.If we are to solve
problemsabouttheseobjects,our workis mademucheasierif we can representtheseobjectsin diagrams.
In fact, for mostof us, diagramsare absolutelyessentialfor problemsolvingin geometry.
BasicPostulates—AnotherLook
Just as undefinedtermsare buildingblocksthat otherdefinitionsare built on, postulatesare the building
blocksof logic.We’re now readyto restatesomeof the basicpostulatesin slightlymoreformalterms,and
to use diagrams.
Postulate 1 Throughany two distinctpoints,thereis exactlyone line.Comment:Any two pointsare collinear.Postulate 2 Thereis exactlyone planethat containsany threenoncollinearpoints.Comment:Sometimesthis is expressedas: “Threenoncollinearpointsdeterminea
plane.”