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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.