Geom. – Ch. 2.4 Biconditional Statementsmaestrodeyo.weebly.com/uploads/1/7/1/0/17102056/... · The biconditional “p if and only if q” can also be written as “p iff q” or

Geom.–Ch.2.4BiconditionalStatements

Mr.Deyo

HomeWork1‐2‐3:1)StormCheckPastedinNotebook?

2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?

Learning Target

Studentswillwriteandanalyzethetruthvalueofbiconditionalstatements.

Studentswillshowthisbycompletingagraphicorganizerandsolvingdeductivereasoningproblemsinapairactivity.

Storm Check (Think, Write, Discuss, Report) Questions on which to ponder and answer: 1.   How are the two pictures similar? 2.   How are they different? 3.   How can these two pictures be related to math?

1)  Inductive2)  Deductive3)  Detachment

4)  Syllogism

Vocabulary 1.  Teachersaystheword.

•  ALLStudentsrepeattheword.

2.  Teachercountsoutsyllablesass/hesaystheword.

•  ALLstudentsrepeatsyllablecountastheysaytheword.

3.  Studentteamscreateaphysicalrepresentationoftheword.

•  ClasschoosesonephysicalrepresentationforALLstudents.

4.  Studentteamscreateafriendlydefinitionfortheword.

•  Classchoosesonefriendlydefinitionfortheword.

DAY 3 and/or DAY 4 1. Review the word

¨ Friendly Definition ¨ Physical Representation

2. Show how the word works ¨ Synonyms/antonym ¨ Word Problems ¨ Related words/phrases ¨ Example/non-example

Friendly Definition Sketch

Wordwork Sentence

DAY 2 1. Review word

¨ Friendly Definition ¨ Physical Representation

2. Draw a sketch

DAY 5 1. Review the word

¨ Friendly definition ¨ Physical Representation

3. Write a sentence  at least 2 rich words (1 action)  correct spelling  correct punctuation  correct subject/predicate agreement  clear and clean writing

DAY 1 1.   Use Visuals

2.   Introduce the word ¨ Friendly Definition ¨ Physical Representation

3.   Use Cognates

4.   Write friendly definition

5.   Physical Representation

WordList1.  2.  3.  4. 

Notes:Whenyoucombineaconditionalstatementanditsconverse,youcreateabiconditionalstatement.Abiconditionalstatementisastatementthatcanbewrittenintheform“pifandonlyifq.”Thismeans“ifp,thenq”and“ifq,thenp.”

pqmeanspqandqp

Thebiconditional“pifandonlyifq”canalsobewrittenas“piffq”orp q.

WritingMath

Forabiconditionalstatementtobetrue,boththeconditionalstatementanditsconversemustbetrue.Ifeithertheconditionalortheconverseisfalse,thenthebiconditionalstatementisfalse.

A‐BProblemAnotes:

1)IfthedateisJuly4th,thenitisIndependenceDayintheU.S.

Fortheconditional,writetheconverseandabiconditionalstatement.

Converse:

Biconditional:

2)Ifpointslieonthesameline,thentheyarecollinear.

Converse:

Biconditional:

A‐BProblemACheck:

1)IfthedateisJuly4th,thenitisIndependenceDayintheU.S.

Fortheconditional,writetheconverseandabiconditionalstatement.

Converse:IfitisIndependenceDayintheU.S.,thenthedateisJuly4th.

Biconditional:ItisJuly4thifandonlyifitisIndependenceDay.

2)Ifpointslieonthesameline,thentheyarecollinear.

Converse:Ifpointsarecollinear,thentheylieonthesameline.

Biconditional:Pointslieonthesamelineifandonlyiftheyarecollinear.

A‐BProblemBSOLVE!!

Foreachconditional,writetheconverseandabiconditionalstatement. 3.If5x–8=37,thenx=9.

Converse:

4.Iftwoangleshavethesamemeasure,thentheyarecongruent.

Converse:

Biconditional:

Biconditional:

A‐BProblemBCheck!!

Foreachconditional,writetheconverseandabiconditionalstatement. 3.If5x–8=37,thenx=9.

Converse:Ifx=9,then5x–8=37.

4.Iftwoangleshavethesamemeasure,thentheyarecongruent.

Converse:Iftwoanglesarecongruent,thentheyhavethesamemeasure.

Biconditional:5x–8=37ifandonlyifx=9.

Biconditional:Twoangleshavethesamemeasureifandonlyiftheyarecongruent.

StormCheck(Think,Write,Discuss,Report)

Whywoulddefinitionsandbiconditionalstatementsberelated?

Ispeculatethatdefinitionsandbiconditional

statementsarerelatedbecause_______________

_________________________________________

_________________________________________.

Notes:

Adefinitionisastatementthatdescribesamathematicalobjectandcanbewrittenasatruebiconditional.Ingeometry,biconditionalstatementsareusedtowritedefinitions.Intheglossary,apolygonisdefinedasaclosedplanefigureformedbythreeormorelinesegments.

Thinkofdefinitionsasbeingreversible.Postulates,howeverarenotnecessarilytruewhenreversed.

HelpfulHint

Atriangleisdefinedasathree‐sidedpolygon,andaquadrilateralisafour‐sidedpolygon.

A‐BProblemAnotes:

Writeeachdefinitionasabiconditionalstatement.

1) A pentagon is a five-sided polygon.

2) A right angle measures 90°.

A‐BProblemACheck:

Writeeachdefinitionasabiconditionalstatement.

1) A pentagon is a five-sided polygon.

2) A right angle measures 90°.

A figure is a pentagon if and only if it is a 5-sided polygon.

An angle is a right angle if and only if it measures 90°.

A‐BProblemBSOLVE!!

3. A quadrilateral is a four-sided polygon.

4. The measure of a straight angle is 180°.

A‐BProblemBCheck!!

3. A quadrilateral is a four-sided polygon.

4. The measure of a straight angle is 180°.

A figure is a quadrilateral if and only if it is a 4-sided polygon.

An angle is a straight angle if and only if its measure is 180°.

StormCheck(Think,Write,Discuss,Report)

Biconditionalstatementsareusedinmakingdefinitions.Whyaredefinitionsandbiconditionalstatementsrelated?

Inmyownwords,definitionsandbiconditional

statementsarerelatedbecause_______________

_________________________________________

_________________________________________.

Vocabulary Review 1.  Teachersaystheword.

•  ALLStudentsrepeattheword.

2.  Teachercountsoutsyllablesass/hesaystheword.

•  ALLstudentsrepeatsyllablecountastheysaytheword.

3.  Studentteamscreateaphysicalrepresentationoftheword.

•  ClasschoosesonephysicalrepresentationforALLstudents.

4.  Studentteamscreateafriendlydefinitionfortheword.

•  Classchoosesonefriendlydefinitionfortheword.

1)  Inductive2)  Deductive3)  Detachment

4)  Syllogism

Learning Target

Studentswillwriteandanalyzethetruthvalueofbiconditionalstatements.

Studentswillshowthisbycompletingagraphicorganizerandsolvingdeductivereasoningproblemsinapairactivity.

2)Section______ 3)Section______RFM/RTProblems_________ NotesCopiedinNotebook?Pasted&SolvedinNotebook?

HomeWork1‐2‐3:1)StormCheckPastedinNotebook?

Ticket OUT.

Write the definition “An acute triangle is a triangle with three acute angles” as a biconditional.

Ticket OUT.

Write the definition “An acute triangle is a triangle with three acute angles” as a biconditional.

A triangle is acute iff it has 3 acute angles.