centimeter.
IdentifyingYour Strategy
At this point,you havesimplifiedthe problemby askingyourselfquestionsaboutit, and createddifferent
representationsof the importantinformation.The time has cometo establisha formalplan of attack.This
is a crucialstep in the problem-solvingprocess,as it lays the groundworkfor your solution.
To organizeyour thoughts,thinkof your geometricknowledgeas a toolbox.Eachtime you learna new
strategy, technique,or concept,add it to your toolbox.Then,whenyou needto solvea problem,you can
selectthe appropriatetool to use.
For now, take a quicklook at the representationsdrawnfor the exampleproblemto identifywhattoolsyou
mightneed.You can use this sectionto clearlyidentifyyour strategy.
Example
Ehabdrewa rectangle on the chalkboard. was and was .If Ehabdrawsin the diagonal ,whatwill be its length?
In the first representation,thereis simplya rectanglewith a diagonal.Thoughthereis a way to solvethis
problemusingthis diagram,it will not be covereduntil later in this book.For now, you do not havethe tools
to solveit.
The seconddiagramshowsthe buildingblocksthat comprisethe rectangle.The diagonalcuts throughthe
blocksbut presentsthe samechallengesas the first diagram.You do not yet havethe toolsto solvethe
problemusingthis diagrameither.
The third diagramshowsa coordinategrid with the rectangledrawnin. The diagonalhas two endpoints
with specificcoordinatepairs.In this chapter, you learnedthe distanceformulato find lengthson a coordinate
grid. This is the tool you needto solvethe problem.
Your strategyfor this problemis to identifythe two endpointsof on the grid as and
. Use the distanceformulato find the length.The resultwill be the solutionto the problem.
MakingCalculations
The last step in any problem-solvingsituationis employingyour strategyto find the answer. Be sure that
you use the correctvaluesas identifiedin the relevantinformation.Whenyou performcalculations,use a
penciland paperto keeptrackof your work.Manycarelessmistakesresultfrom mentalcalculations.Keep
trackof eachstep alongthe way.
Finally, whenyou havefoundthe answer, thereare two morequestionsto ask yourself:
- Did I providethe informationthe problemrequested?
Go backto the first stagesof the problem.Verify that you answeredall partsof the question.
- Doesmy answermakesense?
Your answershouldmakesensein the contextof the problem.If your numberis abnormallylargeor small
in value,checkyour work.
Example