CK12 - Geometry

We saw abovethat the if part of this statement,whichis

If then

This statementis false.One counterexampleis.

Notethat if either or is false,then is false.

LessonSummary

In this lessonyou havelearnedhow to expressmathematicaland otherstatementsin if-thenform.You also

learnedthat eachif-thenstatementis linkedto variationson the basicthemeof “If then .” Thesevariations
are the converse,inverse,and contrapositiveof the if-thenstatement.Biconditionalstatementscombinethe
statementand its converseinto a single“if and only if” statement.Definitionsare an importanttype of bicon-
ditional,or if-and-only-if,statement.

Pointsto Consider

We calledpoints,lines,and planesthe buildingblocksof geometry. We will soonsee that hypothesis,con-
clusion,as well as if-thenand if-and-only-ifstatementsare the buildingblocksthat deductivereasoning,or
logic,is built on. This type of reasoningwill be usedthroughoutyour studyof geometry. In fact, onceyou
understandlogicalreasoningyou will find that you applyit to otherstudiesand to informationyou encounter
all your life.

LessonExercises

Write the hypothesisand the conclusionfor eachstatement.

1. If dividesevenlyinto , then is an evennumber.


2. If a trianglehas threecongruentsides,it is an equilateraltriangle.


3. Allequiangulartrianglesareequilateral.


4. Whatis the converseof the statementin exercise1 above?Is the conversetrue?


5. Whatis the inverseof the statementin exercise2 above?Is the inversetrue?


6. Whatis the contrapositiveof the statementin exercise3? Is the contrapositivetrue?


7. The converseof a statementaboutcollinearpoints , , and is: If and , then

is the midpointof.

• Whatis the statement?


• Is it true?

8. Whatis the inverseof the inverseof if then?


9. Whatis the one-wordnamefor the converseof the inverseof an if-thenstatement?


10. Whatis the one-wordnamefor the inverseof the converseof an if-thenstatement?

For eachof the followingbiconditionalstatements: