- intersects at point.
- True: The Line Postulateimpliesthat you can alwaysdrawa line betweenany two points,so they must
be collinear. - False.Threecollinearpointscouldbe at the intersectionof an infinitenumberof planes.See the images
of intersectingplanesfor an illustrationof this. - For 9 to be true, it shouldread:“Any threenon-collinearpointsdeterminea plane.”
Segmentsand Distance
LearningObjectives
- Measuredistancesusingdifferenttools.
- Understandand applythe ruler postulateto measurement.
- Understandand applythe segmentadditionpostulateto measurement.
- Use endpointsto identifydistanceson a coordinategrid.
Introduction
You havebeenusingmeasurementfor mostof your life to understandquantitieslike weight,time,distance,
area,and volume.Any time you havecookeda meal,boughtsomething,or playeda sport,measurement
has playedan importantrole. This lessonexploresthe postulatesaboutmeasurementin geometry.
MeasuringDistances
Thereare manydifferentwaysto identifymeasurements.This lessonwill presentsomethat may be familiar,
and probablya few that are new to you. Beforewe beginto examinedistances,however, it is importantto
identifythe meaningofdistancein the contextof geometry. The distancebetweentwo pointsis definedby
the lengthof the line segmentthat connectsthem.
The mostcommonway to measuredistanceis with a ruler. Also,distancecan be estimatedusingscaleon
a map.Practicethis skill in the examplebelow.
NotationNotes:Whenwe namea segmentwe use the endpointsand and overbarwith no arrows. For
example,“SegmentAB” is written. The lengthof a segmentis namedby givingthe endpointswithout
usingan overline.For example,the lengthof is written. In somebooksyou may also see
, whichmeansthe sameas , that is, it is the lengthof the segmentwith endpointsA and B.Example 1
Use the scaleto estimatethe distancebetweenAaron’s houseand Bijal’s house.