,*APT] #G3 ,GEOMETRY #G4A = ,ALL ,GRADE ,LEVELS ,NEW ,SYMBOLS ,9TRODUC$ ,%APES .=$ . ,%APE 9DICATOR " .=$C . ,CIRCLE .=$4 . ,SQU>E .=$G . ,P>ALLELOGRAM .=$T . ,TRIANGLE .=$R . ,RECTANGLE .=$D . ,DIAMOND .=$[ . ,ANGLE .=$O . ,"R >R[ "<3TRACT$"> #A ,*APT] #G A#G4A ,SIGNS ( COMP>ISON .=@: . ,SIMIL> TO .=@:.K . ,3GRU5T TO .=/@:.K . ,N 3GRU5T TO .=$L . ,P>ALLEL TO .=$P . ,P]P5DICUL> TO .=/$L . ,N P>ALLEL TO .=/$P . ,N P]P5DICUL> TO ------------------------------------#G4B ,O!R SYMBOLS .=^.* . ,DEGREE SIGN .=' . ,S+LE PRIME .='' . ,D\BLE #B ,*APT] #G A#G4B PRIME .=. . ,GREEK LR 9DICATOR " .=.P . ,PI ,MODIFI$ EXPRES.NS .=" . ,MULTIPURPOSE 9DICATOR " .=< . ,DIRECTLY OV] 9DICATOR " .=% . ,DIRECTLY "U 9DICATOR " .=] . ,T]M9A;N 9DICATOR " ,NEW ,,BANA ,T]MS _4 ^1,%APE ^19DICATOR3 ,%APES1 S* Z A SQU>E OR TRIANGLE1 >E REPRES5T$ 9 BRL US+ ! %APE 9DICATOR FOLL[$ BY A %APE SYMBOL ,- EI A NUMB] OR "O OR M LRS SU7E/IVE ( ! "N ( ! %APE 2+ REPRES5T$4 _4 ^1,ID5TIFI]3 ,:5 A %APE IS FOLL[$ BY "S TYPE ( ID5TIFICA;N S* Z A LR1 #C ,*APT] #G B#G4B SEQU;E ( LRS1 OR A NUMB] "1 ! ID5TIFICA;N IS CALL$ AN ID5TIFI]4 _4 ^7,GREEK LR 9DICATOR^'3 ,LRS ( ! ,GREEK ALPHABET 2G9 ) DOTS #D-#F TO ID5TIFY X Z A ,GREEK LR4 _4 ^1,FIVE-/EP ^1RULE3 ,! FIVE-/EP RULE IS US$ :5 WRIT+ MODIFI$ EXPRES.NS S* Z _% ",A,B<$[33O] _:4 ,X IS CALL$ ! FIVE-/EP RULE 2C "! >E FIVE /EPS T M/ 2 US$ 9 ! SAME ORD] EA* "T AN EXPRES.N IS MODIFI$4 _4 ^1,MULTI-PURPOSE ^19DICATOR3 ,DOT #E IS US$ 9 A V>IETY ( WAYS 9 ,NEME? ,CODE TO AVOID 3FU.N 2T SYMBOLS4 ,X IS AL US$ 2F A MODIFI$ EXPRES.N TO AL]T ! R1D] ( AN UPCOM+ MODIFICA;N4 ------------------------------------#G4C ,KEY ,PO9TS _4 ^1,%APES >E M9IATURE PICTURES ( GEOMETRIC FIGURES OR O!R OBJECTS4 _4 ,2G9N+ 9 F\R? GRADE1 ! ^1%APE ^19DICATOR IS US$ ) A %APE SYMBOL #D ,*APT] #G A#G4C " :5 REPRES5T+ A %APE4 ,"! IS NO PR9T EQUIVAL5T = ! %APE 9DICATOR4 ,:5 A %APE REPRES5TS AN ^1OMIS.N1 ! %APE IS SPAC$ ! SAME WAY Z ! MISS+ ITEM : X REPRES5TS4 _4 ,= /UD5TS 9 ,K9D]G>T5 "? ?IRD GRADE1 MAKE A TACTILE GRAPHIC = ! %APE4 _4 ,:5 A %APE REPRES5TS AN ^1OMIS.N1 ! %APE IS SPAC$ ! SAME WAY Z ! MISS+ ITEM : X REPRES5TS4 _4 ^1,REGUL> ^1POLYGONS "1 ": ALL ANGLES & ALL SIDES >E EQUAL1 >E WRITT5 ) A %APE 9DICATOR FOLL[$ BY ! NUMB] ( SIDES ( ! %APE4 _4 ,TO AVOID 3FU.N1 :5 A NUMB] FOLL[S A REGUL> POLYGON "E"> REPRES5T+ A MISS+ SIGN ( OP]A;N1 A ^1MULTIPURPOSE ^19DICATOR IS PLAC$ 2T ! NUM]IC %APE SYMBOL & ! FOLL[+ NUMB]4 _4 ^1,IRREGUL> ^1POLYGONS & C]TA9 O!R %APES >E WRITT5 ) A %APE 9DICATOR FOLL[$ BY "O OR M LRS OR DOT 3FIGURA;NS SU7E/IVE ( ! "N OR LOOK ( ! PR9T %APE 2+ REPRES5T$ "4 _4 ,PLACE A SPACE 2T ! %APE & XS ^1ID5TIFI] "1 EV5 IF "! IS N A SPACE 9 PR9T4 _4 ,! ^7,5GLI% LR 9DICATOR^' IS N US$ :5 WRIT+ A %APE4 _4 ,A V>IETY ( ^7SIGNS ( COMP>ISON^' "ALLEL TO"> >E US$ 9 GEOMETRY4 ,L1VE A SPACE 2F & AF A SIGN ( COMP>ISON4 _4 ,! ^1DEGREE ^1SIGN IS A SUP]SCRIPT4 _4 ,:5 WRIT+ ^78! M1SURE (0 AN ANGLE^' USE 8;M0 )\T AN ,5GLI% LR 9DICATOR4 ,IF ! 8;M0 IS ITALICIZ$ 9 PR9T1 D N ITALICIZE ! 8;M0 9 BRL4 _4 ,USE A ^1CAPITALIZA;N ^19DICATOR 9 FRONT ( EA* LR :5 BRAILL+ A SEQU;E ( LRS S* Z 9 _% $T ,A,B,C _:4 _4 ,! ^1S+LE ^1PRIME & ^1D\BLE ^1PRIME SIGNS >E US$ = FEET & 9*ES & = M9UTES & SECONDS4 ,"! IS NO SPACE 2T ! S+LE OR D\BLE PRIME SIGNS & ! QUANTITIES TO : !Y APPLY4 #F ,*APT] #G C#G4C _4 ,:5 WRIT+ ^1TRANS=MA;NS1 9CLUDE ! "R >R[ "<3TRACT$"> & R1D X Z 8MAPS TO04 ,USE PRIME NOTA;N AL;G ) ! >R[ TO MAP A ------------------------------------#G4D PRE-IMAGE TO A NEW TRANS=M$ IMAGE " OR EV5 ANO!R TRANS=M$ IMAGE "4 _4 ,USE ! ^7,GREEK LR 9DICATOR^' :5 BRAILL+ ! L[]CASE ,GREEK LR ^1PI4 _4 ,"S ( ! ,NEME? ,CODE SYMBOLS US$ ) MODIFI$ EXPRES.NS 9CLUDE3 ! ^7DIRECTLY OV] 9DICATOR1 DIRECTLY "U 9DICATOR1 HORIZONTAL B>1 TWO-WAY HORIZONTAL >R[1^' & ^7"R >R[ "<3TRACT$">^'4^' _4 ,:5 BRAILL+ ^1MODIFI$ ^1EXPRES.NS FOLL[ ! ^1FIVE-/EP ^1RULE4 ,9TRODUC;N ,/UD5TS >E F/ 9TRODUC$ TO GEOMETRY 9 ,K9D]G>T5 2G9N+ ) BASIC %APES S* Z CIRCLE & SQU>E "<,COMMON ,CORE ,/ATE ,/&>DS ,9ITIATIVE1 #BJAJ2 ,M>YL& ,/ATE ,DE"P;T ( ,$UCA;N1 #BJAE">4 ,= #G ,*APT] #G A#G4D /UD5TS 9 ,K9D]G>T5 "? ?IRD GRADE1 USE MANIPULATIVES OR MAKE A TACTILE GRAPHIC = TWO-DIM5.NAL %APES4 ,= ?REE-DIM5.NAL %APES S* Z A CUBE OR A C"O1 ONLY USE #C,D MANIPULATIVES4 ,G5]AL $UCA;N T1*]S LIKELY H MANIPULATIVES T C 2 US$ ) /UD5TS ) VISUAL IMPAIR;TS4 ,/UD5TS >E 9TRODUC$ TO ADDI;NAL GEOMETRY 3CEPTS 9 F\R? "? EIDS ,9ITIATIVE1 #BJAJ2 ,M>YL& ,/ATE ,DE"P;T ( ,$UCA;N1 #BJAE">4 ,DUR+ HI< S*OOL1 MO/ /UD5TS COMPLETE A GEOMETRY C\RSE "<,COMMON ,CORE ,/ATE ,/&>DS ,9ITIATIVE1 #BJAJ">4 ,%APES ,2G9N+ 9 F\R? GRADE1 ! ^1%APE ^19DICATOR IS US$ ) A %APE SYMBOL " :5 REPRES5T+ A %APE4 ,X TAKES "O CELL TO WRITE ! %APE 9DICATOR 9 ,NEME? ,CODE4 ,X IS WRITT5 ) DOTS #A-#B-#D-#F4 .=$ ,"! IS NO PR9T EQUIVAL5T TO ! #H ,*APT] #G B#G4D %APE 9DICATOR4 ,X IS PAIR$ ) ! SYMBOL REPRES5T+ ! %APE4 ,REGUL> POLYGONS "1 ": ALL ANGLES & ALL SIDES >E EQUAL1 >E WRITT5 ) ! %APE 9DICATOR FOLL[$ BY ! NUMB] ( SIDES ( ! %APE "<,RULE ,,XVI1 ^S#AJF & ^S#AJI">4 ,NOTICE T A NUM]IC 9DICATOR IS N US$4 .=$4 ,SQU>E .=$5 ,P5TAGON .=$6 ,HEXAGON ------------------------------------#G4E ,IRREGUL> POLYGONS & C]TA9 O!R %APES >E WRITT5 ) ! %APE 9DICATOR FOLL[$ BY ! SYMBOL T REPRES5TS ! %APE4 ,! %APE SYMBOL IS COMPOS$ ( "O OR M LRS OR DOT 3FIGURA;NS SU7E/IVE ( ! "N OR LOOK ( ! PR9T %APE 2+ REPRES5T$ "<,RULE ,,XVI1 ^S#AJF & ^S#AJG">4 .=$C ,CIRCLE .=$G ,P>ALLELOGRAM .=$T ,TRIANGLE .=$R ,RECTANGLE .=$D ,DIAMOND .=$[ ,ANGLE #I ,*APT] #G A#G4E .=$O ,"R >R[ "<3TRACT$"> ,:5 BRAILL+ A %APE1 D N PUT A SPACE 2T ! %APE 9DICATOR & ! SYMBOL T REPRES5TS ! %APE4 ,H["E1 PUT A SPACE 2T ! %APE SYMBOL & XS ID5TIFI] " T FOLL[ X"> EV5 IF X DOES N LOOK L "! IS "O 9 PR9T "<,RULE ,,XVI1 ^S#AAE;A">4 ,= 9/.E 9 _% $T ,A,B,C _: "1 "! IS A SPACE 2T ! TRIANGLE & ! LRS T FOLL[ X 9 BRL4 ,EA* LR M/ 2 9DIVIDUALLY CAPITALIZ$1 & ITALICS >E N US$ "<,,BANA ,GUID.E1 #BJAH1 ;P4 #H">4 ,H["E1 D N R1D ! LRS Z CAPITALIZ$ LRS4 ,EXAMPLE #G4A 3TA9S FIVE EXAMPLES ( %APES4 ,NOTICE T 9 ! SECOND EXAMPLE "! DOES N APPE> TO 2 A SPACE 2T ! CIRCLE SYMBOL & ! LR ;,S 9 PR9T4 ,H["E1 A SPACE HAS BE5 US$ 9 BRL4 ,9 ! EXAMPLES1 ! LRS >E ITALICIZ$ 9 PR9T1 B !Y >E N ITALICIZ$ 9 BRL4 #AJ ,*APT] #G B#G4E ,EXAMPLE #G4A _% $[ ,B $C ,S ------------------------------------#G4F $T ,A,B,C $[ #1 $4 ,E,F,G,H _: ,SIGNS ( ,COMP>ISON ,US$ 9 ,GEOMETRY ,/UD5TS >E F/ 9TRODUC$ TO ! FOLL[+ SYMBOLS 9 SEV5? OR EI TO1 3GRU5T TO1 & N 3GRU5T TO "<,COMMON ,CORE ,/ATE ,/&>DS ,9ITIATIVE1 #BJAJ2 ,M>YL& ,/ATE ,DE"P;T ( ,$UCA;N1 #BJAE">4 ,^! SYMBOLS >E SIGNS ( COMP>ISON4 ,X TAKES TWO CELLS TO WRITE ! ^1SIMIL> ^1TO SYMBOL 9 ,NEME? ,CODE4 ,9 PR9T1 X IS "S"TS CALL$ A TILDE4 ,X IS WRITT5 ) DOT #D1 FOLL[$ BY DOTS #A-#E-#F4 .=@: ,X TAKES F\R CELLS TO WRITE ! ^13GRU5T ^1TO SYMBOL 9 ,NEME? ,CODE4 ,! 3GRU5T TO SYMBOL IS A COMB9A;N ( ! TILDE & ! #AA ,*APT] #G A#G4F EQUALS SIGN4 ,X IS WRITT5 ) DOT #D1 FOLL[$ BY DOTS #A-#E-#F1 !N DOTS #D-#F1 FOLL[$ BY DOTS #A-#C4 .=@:.K ,X TAKES FIVE CELLS TO WRITE ! ^7N 3GRU5T TO^' SYMBOL 9 ,NEME? ,CODE4 ,X IS WRITT5 ) DOTS #C-#D1 FOLL[$ BY DOT #D1 FOLL[$ BY DOTS #A-#E-#F1 FOLL[$ BY DOTS #D-#F1 FOLL[$ BY DOTS #A-#C4 .=/@:.K ^1,T1*+ ^1,TIP3 ,COMP>ISON SIGNS C 2 NEGAT$ BY PLAC+ DOT #C-#D 2F ! SYMBOL 9 ,NEME? ,CODE4 ,"!=E1 ! IS N 3GRU5T TO SYMBOL & ! N EQUAL TO SYMBOL BO? 2G9 ) DOTS #C-#D4 ------------------------------------#G4G ,EXAMPLE #G4B 3TA9S ?REE EXAMPLES %[+ ^! NEW SIGNS ( COMP>ISON US$ 9 GEOMETRY4 ,NOTICE "! IS A SPACE 2F & AF SIGNS ( COMP>ISON4 #AB ,*APT] #G A#G4G ,EXAMPLE #G4B _% $[ #1 @:.K $[ #2 $[ ,A /@:.K $[ ,B $G ,A,B,C,D @: $G ,W,X,Y,Z _: ,PRACTICE #G4A ,9T]L9E ! FOLL[+ PROBLEMS T 3TA9 %APES4 _% #1_4 $C ,P #2_4 $[ #1 /@:.K $[ #3 #3_4 $4 ,A,B,C,D @: $4 ,E,F,G,H #4_4 $T ,L,M,N @:.K $T ,P,Q,R _: ,USE YR BRLWRIT] TO WRITE ! FOLL[+ PROBLEMS T 3TA9 %APES4 @.<,! MA? 3T5T 2L HAS BE5 SPELL$ \ TO ALL[ = PRACTICE4@.> #A4 ,CIRCLE ;,Q #B4 ,TRIANGLE ,,DEF IS SIMIL> TO TRIANGLE ,,XYZ #C4 ,SQU>E ,,PQRS IS 3GRU5T TO SQU>E ,,ABCD #D4 ,ANGLE #B IS N 3GRU5T TO #AC ,*APT] #G B#G4G ANGLE #G ,! ,M1SURE ( AN ,ANGLE ,! LR ;M 9 FRONT ( AN ANGLE NOTA;N M1NS 8^7! M1SURE (4^'0 ,! ,5GLI% LR 9DICATOR IS N US$ ) ! LR ;M4 ,AL D N ITALICIZE ! LR ;M1 EV5 IF X APPE>S 9 ITALICS 9 PR9T4 ------------------------------------#G4H ,! ^1DEGREE ^1SIGN IS (T5 US$ :5 WRIT+ ! M1SURE ( AN ANGLE4 ,Z PREVI\SLY COV]$ 9 ,*APT]S #C & #F1 X TAKES ?REE CELLS TO WRITE ! ^1DEGREE ^1SIGN 9 ,NEME? ,CODE4 ,X IS WRITT5 ) DOTS #D-#E1 FOLL[$ BY DOTS #D-#F1 FOLL[$ BY DOTS #A-#F4 .=^.* ^1,T1*+ ^1,TIP3 _% $[ ,A,B,C _: TRIANGLE " D5OTES ! ANGLE XF1 ":AS _% M$[ ,A,B,C _: " IS XS M1SURE4 ,ANGLES C 2 3GRU5T TO EA* O!R1 & ! M1SURES ( ANGLES C 2 EQUAL TO EA* O!R4 #AD ,*APT] #G A#G4H ,EXAMPLE #G4C 3TA9S ?REE EXAMPLES T 9CLUDE A M1SURE ( AN ANGLE4 ,NOTICE T ! DEGREE SIGN IS N US$ 9 ! SECOND EXAMPLE4 ,EXAMPLE #G4C _% M$[ #1 .K #60^.* M$[ #3 .K M$[ #5 M$[ ,X,Y,Z .K #120^.* _: ,US+ ,SIGNS ( ,OP]A;N ) ,M1SURES ( ,ANGLES ,D N PUT A SPACE 2T M1SURES ( ANGLES & A SIGN ( OP]A;N4 ,EXAMPLE #G4D PROVIDES TWO EXAMPLES ( M1SURES ( ANGLES US$ ) SIGNS ( OP]A;N4 ,EXAMPLE #G4D _% M$[ #3-M$[ #4 .K #30^.* ------------------------------------#G4I M$[ ,X,W,Y+M$[ ,Y,W,Z .K M$[ ,X,W,Z _: ,%APES ,T ,REPRES5T ,OMIS.N ,Z A REM9D]1 :5 A %APE IS US$ TO #AE ,*APT] #G A#G4I REPRES5T A SIGN ( OMIS.N 9 ,K9D]G>T5 "? ?IRD GRADE 9/RUC;NAL MAT]IALS1 ! ACTUAL %APE IS PRODUC$ = ! BRL R1D]4 ,! %APE C 2 PRODUC$ US+ GRAPHIC >T TAPE1 FELT1 /ICK]S ETC4 ,%APE SYMBOLS MAY 2 US$ 9 MAT]IALS = /UD5TS 9 F\R? GRADE & ABV4 ,:5 US+ %APES TO REPRES5T OMIS.N1 SPACE !M ! SAME WAY T ! ITEM !Y REPLAC$ WD 2 SPAC$4 ,EXAMPLE #G4E 3TA9S F\R PROBLEMS 9 : A %APE IS US$ TO REPRES5T OMIS.N = /UD5TS 9 F\R? GRADE & ABV4 ,NOTICE ! SQU>E & RECTANGLE REPRES5T A SIGN ( COMP>ISON 9 ! F/ & SECOND PROBLEMS4 ,"!=E1 "! IS A SPACE ON EI SIDE ( ! %APE SYMBOL4 ,9 ! ?IRD EXAMPLE1 ! %APE REPRES5TS A MISS+ NUMB] S "! IS NO SPACE 2T X & ! MULTIPLICA;N SIGN4 ,9 ! F\R? EXAMPLE1 ! %APE REPRES5TS A SIGN ( OP]A;N S "! IS NO SPACE 2T ! TRIANGLE & ! LRS T PREC$E & FOLL[ X4 ,EXAMPLE #G4E _% $[ #1 $4 $[ #5 #AF ,*APT] #G B#G4I M$[ ,A,B,C $R #20^.* #4@*$C .K #12 X$TY .K XY _: -----------------------------------#G4AJ ,USE ( ! ,MULTIPURPOSE ,9DICATOR ) ,REGUL> ,POLYGONS ,REGUL> POLYGONS1 S* Z ! SQU>E1 >E REPRES5T$ BY ! %APE 9DICATOR FOLL[$ BY A NUMB]4 ,9 ! CASE ( A SQU>E1 ! NUMB] IS #D4 ,TO AVOID 3FU.N1 :5 A NUMB] FOLL[S A REGUL> POLYGON REPRES5T+ A MISS+ SIGN ( OP]A;N1 A MULTIPURPOSE 9DICATOR IS PLAC$ 2T ! %APE SYMBOL & ! NUMB] "<,RULE ,,XXIII1 ^S#AGGVIII">4 ,EXAM9E ! PROBLEM @.;Y@.> N9ETY-TWO @.E@.> EI POLYGON ) #DH SIDES EQUALS #AJJ40 ,AL? "! IS S* A ?+ Z A #DH-GON1 T #AG ,*APT] #G A#G4AJ IS DEF9ITELY N :AT ! MA? T1*] 9T5D$ /UD5TS TO R1D6 ,BY PLAC+ ! MULTIPURPOSE 9DICATOR 2T ! SQU>E & ! #H1 ! BRL R1D] IS AL]T$ TO ! %APE 5D+ & ! NUMB] 2G9N+1 9 ? CASE ! NUMB] #H4 ,EXAM9E ! PROBLEM TRANSCRIB$ CORRECTLY 2L & NOTE ! MULTIPURPOSE 9DICATOR HAS BE5 PLAC$ 2T #D & ! #H4 _% #92$4"8 .K #100 _: ,! MULTIPURPOSE 9DICATOR IS ONLY US$ ) A REGUL> POLYGON :5 ! ITEM FOLL[+ ! REGUL> POLYGON1 REPRES5T+ A MISS+ SIGN ( OP]A;N1 IS A NUMB]4 ,EXAMPLE #G4F 3TA9S F\R PROBLEMS4 ,NOTICE 9 ! F/ & SECOND PROBLEMS1 ! REGUL> POLYGONS "ES"> >E FOLL[$ BY NUMB]S S ! MULTIPURPOSE 9DICATOR IS US$4 ,9 ! ?IRD PROBLEM1 ! REGUL> POLYGON IS N FOLL[$ BY A NUMB] S ! MULTIPURPOSE 9DICATOR IS N US$4 ,9 ! F9AL PROBLEM1 ! MULTIPURPOSE 9DICATOR IS US$ 2C ! HEXAGON " IS FOLL[$ BY A NUMB]4 #AH ,*APT] #G B#G4AJ ,EXAMPLE #G4F _% X+4$4"3 .K #15 #20 .K #80$4"4 -----------------------------------#G4AA ?10/50# .K ?1/$4# #24$6"4 .K #6 _: ,PRACTICE #G4B ,9T]L9E ! FOLL[+ PROBLEMS T 3TA9 %APES4 _% #1_4 M$[ ,D,E,F .K #45^.* #2_4 #65 .1: #84$4"2 #3_4 M$[ #6-M$[ #3 .K #90^.* #4_4 ?$4/3# .K ?4/6# _: ,USE YR BRLWRIT] TO WRITE ! FOLL[+ PROBLEMS T 3TA9 %APES4 @.<,! MA? 3T5T 2L HAS BE5 SPELL$ \ TO ALL[ = PRACTICE4@.> #A4 ,! M1SURE ( ANGLE ,,LMN PLUS ! M1SURE ( ANGLE ,,PQR EQUALS SIXTY-?REE DEGREES #B4 ,FIFTY @.E@.> FIVE IS N #AI ,*APT] #G A#G4AA EQUAL TO "O HUNDR$ @. T5 #C4 ,! M1SURE ( ANGLE EIE@.> OV] SIX ,SIGNS ( ,%APE ,SURR.D$ BY ,TEXT ,SIGNS ( %APE >E MA!MATICAL2 "!=E1 !Y M/ 2 5CLOS$ 9 ,NEME? ,CODE SWIT* 9DICATORS4 ,REMEMB]1 KEEP ! OP5+ ,NEME? ,CODE 9DICATOR1 ! MA? 3T5T1 & ! ,NEME? ,CODE T]M9ATOR ON ! SAME L9E IF POSSIBLE "<,,BANA ,GUID.E1 #BJAH1 ;P4 #D">4 ,A %APE SYMBOL & XS ID5TIFI] >E 3SID]$ A S+LE ITEM 9 ,NEME? ,CODE1 S D N DIVIDE ! %APE 9DICATOR SYMBOL & XS ID5TIFI] 2T L9ES4 ,EXAMPLE #G4G 3TA9S TWO ^W PROBLEMS 9 : %APES >E SURR.D$ BY TEXT4 ,9 ! F/ ^W PROBLEM1 ! %APE SYMBOL & XS ID5TIFI] >E PLAC$ ON ! SECOND L9E ( BRL4 ,9 ! SECOND ^W PROBLEM1 ! MA? 3T5T IS DIVID$ ACR L9ES S9CE X WD N FIT ON A S+LE L9E4 ,X IS P]MISSIBLE TO H ! ,NEME? #BJ ,*APT] #G B#G4AA T]M9ATOR & FOLL[+ PUNCTUA;N ON A L9E BY !MVS4 -----------------------------------#G4AB ,EXAMPLE #G4G #A4 ,"N ! P>ALLEL SIDES ( _% $R ,A,B,C,D _:4 #B4 ,9 _% $G ,W,X,Y,Z, ,'": M$[ ,W .K #135^.*, ,'F9D M$[ ,Z _:4 ,PRACTICE #G4C ,9T]L9E ! FOLL[+ PROBLEMS T 3TA9 %APES SURR.D$ BY TEXT4 #I4 _% $T ,A,B,C _: IS 3GRU5T TO _% $T ,D,E,F _:4 #AJ4 ,IF _% $[ ,A ,'& $[ ,C _: >E COMPLE;T>Y ANGLES1 !N _% M$[ ,A+M$[ ,C .K #90^.* _:4 ,USE YR BRLWRIT] TO WRITE ! FOLL[+ DIREC;NS & PROBLEMS T 3TA9 %APES SURR.D$ BY TEXT4 @.<,! MA? 3T5T 2L HAS BE5 SPELL$ \ TO ALL[ = PRACTICE4 ,? 9CLUDES #BA ,*APT] #G A#G4AB ! SIGNS ( OP]A;N " LI/$ 9 ! DIREC;NS T FOLL[4@.> ,9 ! NEXT PROBLEMS1 @.E@.> REPRES5TS A SIGN ( OP]A;N4 ,IS X PLUS1 M9US1 "TS1 OR DIVID$-BY8 ,FILL 9 ! BOX ) ! CORRECT SIGN ( OP]A;N4 #A4 ,IF ANGLE ,,PAQ & ANGLE ,,QAR >E A L9E> PAIR1 !N ! M1SURE ( ANGLE ,,PAQ @.E@.> ! M1SURE ( ANGLE ,,QAR EQUALS "O HUNDR$ EIE A L9E> PAIR1 !N "O HUNDR$ EIE@.> ! M1SURE ( ANGLE ,,QAR EQUALS ! M1SURE ( ANGLE ,,PAQ4 ,4T.E ,2T ,TWO ,PO9TS ,9 GEOMETRY1 :5 TWO CAPITAL LRS >E WRITT5 SIDE BY SIDE ) NO MODIFICA;N "1 ? REPRES5TS ! 4T.E 2T PO9T ,A & PO9T ;,B4 ,S9CE 4T.E IS A M1SURE1 SIGNS ( OP]A;N C 2 US$ ) 4T.ES1 SIMIL> TO US+ SIGNS ( OP]A;N ) #BB ,*APT] #G B#G4AB M1SURES ( ANGLES4 -----------------------------------#G4AC ,= EXAMPLE1 _% ,A,B+,B,C .K ,A,C _: ,EA* LR M/ 2 9DIVIDUALLY CAPITALIZ$1 & ITALICS >E N US$4 ,? PROBLEM IS R1D 8;,,AB PLUS ,,BC EQUALS ;,,AC04 ,H["E1 D N R1D ! 4T.ES Z CAPITALIZ$ LRS4 ^1,T1*+ ^1,TIP3 ,PO9T \ TO /UD5TS T S9CE EA* PO9T HAS XS [N SEP>ATE LABEL1 EA* LR NE$S XS [N CAPITAL LR 9DICATOR4 ,EXAMPLE #G4H 3TA9S ?REE EXAMPLES ( 4T.E 2T TWO PO9TS4 ,NOTICE T ! EXAMPLES >E N NUMB]$ & "!=E >E =MATT$ Z P>AGRAPHS ) ! F/ L9E 2G9N+ 9 CELL #C & RUNOV] L9ES 2G9N+ 9 CELL #A4 ,EXAMPLE #G4H _% ,A,C-,A,B .K ,B,C _: ,IF _% ,P,Q .K ,Q,R _: & ;,Q IS 2T ;,P & ;,R1 :AT IS ANO!R "N = PO9T ;,Q8 ,IF #BC ,*APT] #G A#G4AC _% ,A,C .K #5, ,B,C .K #9 _:1 & ;,B IS 2T ,A & ;,C1 :AT IS _% ,A,B _:8 ,S+LE & ,D\BLE ,PRIME ,SIGNS ,/UD5TS 2G9 M1SUR+ ! L5G?S ( OBJECTS Z E>LY Z ! SECOND GRADE & 2G9 M1SUR+ ANGLES Z E>LY Z F\R? GRADE "<,COMMON ,CORE ,/ATE ,/&>DS ,9ITIATIVE1 #BJAJ2 ,M>YL& ,/ATE ,DE"P;T ( ,$UCA;N1 #BJAE">4 ,Z !Y 2COME M EXP]I;ED ) M1SUR+1 /UD5TS >E 9TRODUC$ TO ! S+LE PRIME SIGN & D\BLE PRIME SIGN REPRES5T+ FEET & 9*ES OR M9UTES & SECONDS4 -----------------------------------#G4AD ,X TAKES "O CELL TO WRITE ! ^7S+LE PRIME SIGN^' 9 ,NEME? ,CODE4 ,X IS WRITT5 ) DOT #C4 .=' ,X TAKES TWO CELLS TO WRITE ! ^7D\BLE PRIME SIGN^' 9 ,NEME? ,CODE4 ,X IS WRITT5 ) DOT #C1 FOLL[$ BY DOT #C4 .='' ,"! IS NO SPACE 2T A PRIME SIGN & ! QUANT;Y TO : X APPLIES "<,RULE #BD ,*APT] #G A#G4AD ,,XXII1 ^S#AGB">4 ,EXAMPLE #G4I 3TA9S F\R EXAMPLES US+ ! S+LE & D\BLE PRIME SIGNS4 ,NOTICE T ! F/ TWO EXAMPLES USE ! PRIME SIGNS TO REPRES5T FEET & 9*ES :ILE ! ?IRD & F\R? EXAMPLES USE ! PRIME SIGNS TO REPRES5T M9UTES & SECONDS4 ,AL1 A BASEL9E 9DICATOR " IS REQUIR$ AF ! DEGREE SIGN 9 ! ?IRD & F\R? EXAMPLES S T ! NUMB] FOLL[+ ! DEGREE SIGN IS ON ! BASEL9E4 ,EXAMPLE #G4I _% #6'4'' ,C,D .K #9'10'' #36^.*"30'15'' M$[ ,C .K #44^.*"10'35'' _: -----------------------------------#G4AE ,TRANS=MA;NS ,/UD5TS >E 9TRODUC$ TO ^1TRANS=MA;NS 9 EIDS ,9ITIATIVE1 #BJAJ2 ,M>YL& ,DE"P;T ( ,$UCA;N1 #BJAE">4 #BE ,*APT] #G A#G4AE ,GEOMETRIC TRANS=MA;NS 9VOLVE TAK+ A PREIMAGE & TRANS=M+ X 9 "S WAY TO PRODUCE AN IMAGE^24 ,9 ! FOLL[+ EXAMPLE1 _% $T ,A,B,C _: HAS BE5 ROTAT$ _% #180^.* _: AB ! ORIG9 & !N TRANSLAT$ #B UNITS UP & #A UNIT TO ! LEFT TO CR1TE _% $T ,A',B',C' _:4 #BF ,*APT] #G B#G4AE @.<,? BRL PAGE %D 2 REMOV$ & REPLAC$ ) ! PROVID$ TACTILE GRAPHIC FILE4@.> #BG ,*APT] #G C#G4AE ,PRIME NOTA;N & AN >R[ >E US$ TO MAP ? PRE-IMAGE TO ! NEW TRANS=M$ IMAGE4 _% $T ,A,B,C $O $T ,A',B',C' _: ,9 ,NEME? ,CODE1 ! "R >R[ "<3TRACT$"> IS US$ TO DESIGNATE ? MAPP+ >R[4 ,X TAKES TWO CELLS TO WRITE ! ^7"R >R[ "<3TRACT$">^' 9 ,NEME? ,CODE4 ,X IS WRITT5 ) DOTS #A-#B-#D-#F1 FOLL[$ BY DOTS #A-#C-#E4 .=$O ,:5 R1D+ A TRANS=MA;N1 ! 3TRACT$ "R >R[ IS R1D Z 8MAPS TO04 ,"!=E1 _% $T ,A,B,C $O $T ,A',B',C' _: IS R1D Z 8TRIANGLE ,,ABC MAPS TO TRIANGLE ,A PRIME ;,B PRIME ;,C PRIME10 & X IS BRLD Z3 _% $T ,A,B,C $O $T ,A',B',C' _: -----------------------------------#G4AF ,EXAMPLE #G4AJ 3TA9S TWO EXAMPLES ( TRANS=MA;NS4 ,! SECOND EXAMPLE IS TRANSCRIB$ TWICE4 ,BO? TRANSCRIP;NS >E CORRECT S9CE ! .7#BJAH ,GUID.E = ,TRANSCRIP;N ,US+ ! ,NEME? ,CODE )9 ,,UEB ,3TEXTS.' PROVIDES "S FLEXIBIL;Y AB ": SWIT* 9DICATORS %D 2 PLAC$4 #BH ,*APT] #G A#G4AF ,H["E1 ! SECOND TRANSCRIP;N SAVES A L9E 9 BRL4 ^1,T1*+ ^1,TIP3 ,X IS IMPORTANT T /UD5TS SEE MULTIPLE WAYS ( TRANSCRIB+ ! SAME ?+1 S* Z A TRANS=MA;N4 ,TAKE "T TO FAMILI>IZE /UD5TS ) DI6]5T WAYS TO PRES5T ! SAME MAT]IAL S T IF !Y COME ACR DI6]5T PRES5TA;NS ON TE/S OR 9 TEXTBOOKS1 !Y >E ABLE TO R1D & "U/& !M4 ,EXAMPLE #G4AJ _% $T ,D,E,F $O $T ,D',E',F' $O $T ,D'',E'',F'' ,DRAW A TRANS=MA;N ( _% $G ,A,B,C,D $O $G ,A',B',C',D' _: T IS A TRANSLA;N LEFT _% #2'' _:4 OR @.<,9 ! PR9T COPY1 8OR0 IS WRITT5 9 PR9T 9 ! MIDDLE ( ! BRL EXAMPLES 9 ORD] TO SEP>ATE ! TWO POSSIBLE TRANSCRIP;NS4@.> ,DRAW A TRANS=MA;N ( #BI ,*APT] #G B#G4AF _% $G ,A,B,C,D $O $G ,A',B',C',D' _: T IS A TRANSLA;N LEFT _% #2'' _:4 ,PI ,/UD5TS >E 9TRODUC$ TO ! L[]CASE ,GREEK LR PI 9 SEV5? GRADE1 Z !Y SOLVE PROBLEMS 9VOLV+ CIRCLES1 ! >EA ( A CIRCLE1 & ! VOLUME ( A SP"H "<,COMMON ,CORE ,/ATE ,/&>DS ,9ITIATIVE1 #BJAJ2 ,M>YL& ,DE"P;T ( ,$UCA;N1 #BJAE">4 ,:5 WRIT+ ANY ,GREEK LR1 2G9 ) ! ,GREEK LR 9DICATOR4 ,X IS WRITT5 ) DOTS #D-#F4 ,"! IS NO PR9T EQUIVAL5T = ! ,GREEK LR 9DICATOR4 .=. -----------------------------------#G4AG ,! L[]CASE ,GREEK LR ^1PI1 IS WRITT5 ) DOTS #D-#F1 FOLL[$ BY ! LR 8;P0 : IS DOTS #A-#B-#C-#D4 ,PI IS A POPUL> 3/ANT & IS ! RATIO ( ! CIRCUMF];E ( ANY CIRCLE TO ! DIAMET] ( T CIRCLE4 .=.P ,PI IS US$ 9 GEOMETRY =MULAS S* Z3 _% ,C .K .PD #CJ ,*APT] #G A#G4AG ,A .K .PR^2 ,V .K ?4/3#.PR^3 _: ,EXAMPLE #G4AA 3TA9S TWO EXAMPLES ( ^W PROBLEMS T USE ! ,GREEK LR PI4 ,NOTICE T ! ,NEME? ,CODE SWIT* 9DICATORS & MA? 3T5T >E KEPT ON ! SAME L9E 9 BO? EXAMPLES4 ,EXAMPLE #G4AA #A4 ,IF ! RADIUS ( _% $C ,P ,'IS #3.5 _:1 F9D ! >EA ( _% $C ,P _:1 US+ ! =MULA _% ,A .K .PR^2 _:4 #B4 ,US+ ! =MULA _% ,V .K ?4/3#.PR^3 _:1 F9D ! VOLUME ( A SP"H IF _% R .K #1'2'' _:4 -----------------------------------#G4AH ,PRACTICE #G4D ,9T]L9E ! FOLL[+ PROBLEMS T 3TA9 4T.E 2T PO9TS1 PRIME SIGNS1 TRANS=MA;NS1 & PI4 _% #1_4 ,A,B .K #13'6'' #2_4 M$[ ,D .K #45^.*"10'25'' #CA ,*APT] #G A#G4AH #3_4 $T ,X,Y,Z $O $T ,X',Y',Z' $O $T ,X'',Y'',Z'' #4_4 ,C .K #2.PR _: ,USE YR BRLWRIT] TO WRITE ! PROBLEMS T 3TA9 4T.E 2T PO9TS1 PRIME SIGNS1 TRANS=MA;NS1 & ! ,GREEK LR PI4 @.<,! MA? 3T5T 2L HAS BE5 SPELL$ \ TO ALL[ = PRACTICE4 ,HYPH5S >E US$ TO KEEP FRAC;N & EXPON5T 3T5T TGR4@.> #A4 ,,PQ EQUALS EIR[ RECTANGLE ;,W PRIME ;,X PRIME ;,Y PRIME ;,Z PRIME @.E UNSPAC$ 9 PR9T4@.> #C4 ,! M1SURE ANGLE ,,DEF IS EQUAL TO ?IRTY-F\R DEGREES FIFTY-TWO M9UTES & F\RTE5 SECONDS #D4 ;,V EQUALS "O-OV]-?REE PI ;R SUP]-TWO ;H ,MODIFI$ ,EXPRES.NS ,/UD5TS >E 9TRODUC$ TO MODIFI$ #CB ,*APT] #G B#G4AH EXPRES.NS Z E>LY Z F\R? GRADE "<,COMMON ,CORE ,/ATE ,/&>DS ,9ITIATIVE1 #BJAJ2 ,M>YL& ,DE"P;T ( ,$UCA;N1 #BJAE">4 ,9 PR9T1 A MODIFI$ EXPRES.N IS =M$ :5 A SYMBOL OR COMB9A;N ( SYMBOLS >E PLAC$ DIRECTLY OV] OR "U XS RELAT$ SYMBOL OR EXPRES.N4 ,"S COMMON MODIFI]S >E3 _4 ,! HORIZONTAL B>1 : C 2 PLAC$ OV] AN EXPRES.N OR NUMB] TO REPRES5T A L9E SEG;T OR REP1T+ DIGITS 9 A NUMB] " _4 ,! B>B$ >R[ AT BO? 5DS TO REPRES5T A L9E " _4 ,! "R PO9T+ >R[ TO REPRES5T A RAY " ,:5 TRANSCRIB+ MO/ MODIFI$ EXPRES.NS 9 ,NEME? ,CODE1 ! ^1FIVE-/EP ^1RULE IS US$ "<,RULE ,,XIV1 ^S#HF">4 ,X IS CALL$ ! FIVE-/EP RULE 2C "! >E FIVE /EPS T M/ 2 US$ 9 ! SAME ORD] EA* "T AN #CC ,*APT] #G C#G4AH EXPRES.N IS -----------------------------------#G4AI MODIFI$ US+ SPECIFI$ SYMBOLS "<,RULE ,,XIV1 ^S#HF">4 ,"! IS NO PR9T EQUIVAL5T = ! F\R MODIFICA;N 9DICATORS4 ,FIVE-,/EP ,RULE ,/EP #A3 ,MULTIPURPOSE 9DICATOR " .=" ,/EP #B3 ,EXPRES.N 2+ MODIFI$ ,/EP #C3 ,DIRECTLY OV] 9DICATOR " .=< OR ,DIRECTLY "U 9DICATOR " .=% ,/EP #D3 ,MODIFI] ,/EP #E3 ,T]M9A;N 9DICATOR " .=] ,COMMON ,MODIFI]S 9 ,GEOMETRY ,! F\R? /EP REQUIRES A MODIFI]4 #CD ,*APT] #G A#G4AI ,?REE COMMONLY US$ MODIFI]S 9 GEOMETRY >E ! HORIZONTAL B>1 B>B$ >R[ AT BO? 5DS1 & "R >R[ "<3TRACT$">4 ,! ^1HORIZONTAL ^1B> IS WRITT5 ) DOTS #A-#E-#F4 .=: ,! ^7B>B$ >R[ AT BO? 5DS^' IS WRITT5 US+ FIVE CELLS4 ,X IS WRITT5 ) DOTS #A-#B-#D-#F1 DOTS #B-#D-#F1 DOTS #B-#E1 DOTS #B-#E1 & DOTS #A-#C-#E4 ,? SYMBOL 2G9S ) ! %APE 9DICATOR1 B NOTICE H[ ! REMA9+ F\R CELLS VISUALLY LOOK L ! PR9T L9E !Y >E REPRES5T+4 .=$[33O -----------------------------------#G4BJ ,Z PREVI\SLY NOT$1 ! ^7"R >R[ "<3TRACT$">^' IS WRITT5 US+ TWO CELLS4 ,X IS WRITT5 ) DOTS #A-#B-#D-#F1 FOLL[$ BY DOTS #A-#C-#E4 ,? SYMBOL AL 2G9S ) ! %APE 9DICATOR1 B NOTICE T ! NEXT CELL VISUALLY LOOKS L A "R-PO9T+ >R[H1D4 ,9 ! EXAMPLE 2L1 ! "R >R[ "<3TRACT$"> REPRES5TS A RAY4 .=$O #CE ,*APT] #G A#G4BJ ,EXAMPLE #G4AB 3TA9S ?REE MODIFI$ EXPRES.NS T MI _% ",P,Q<$[33O] _: " _% ",X,Y<$O] _: " ,MODIFI$ ,EXPRES.NS ,\TSIDE ( ,GEOMETRY ,MODIFI$ EXPRES.NS >E US$ \TSIDE ( GEOMETRY1 9CLUD+ :5 TRANSCRIB+ MULTI-DIGIT REP1T+ DECIMALS4 ,IF A HORIZONTAL B> IS PLAC$ OV] TWO OR M DIGITS 9 A DECIMAL NUMB]1 ! FIVE-/EP RULE M/ 2 FOLL[$4 ,EXAMPLE #G4AC 3TA9S TWO EXAMPLES ( MULTI-DIGIT REP1T+ DECIMALS4 #CF ,*APT] #G B#G4BJ ,EXAMPLE #G4AC _% #20.48"46<:] _: " _% #0."317<:] _: " -----------------------------------#G4BA ,EXCEP;NS TO ! ,FIVE-,/EP ,RULE ,IF A HORIZONTAL B> IS PLAC$ OV] A S+LE DIGIT 9 A DECIMAL NUMB]1 D N USE ! FIVE-/EP RULE4 ,= EXPRES.NS ) ONLY "O REP1T+ DIGIT1 "! IS A 3TRACT$ =M T MAKES !M EASI] & QK] TO R1D4 ,SIMPLY PLACE ! HORIZONTAL B> SYMBOL IMMLY AF ! DIGIT OR LR X MODIFIES "<,RULE ,,XIV ^S#HF;C">4 ,= EXAMPLE1 _% #0.3: _: IS R1D Z Z]O PO9T ?REE ) ! ?REE REP1T+4 ,X IS TRANSCRIB$3 _% #0.3: _: ,EXAMPLE #G4AD 3TA9S TWO EXAMPLES %[+ A HORIZONTAL B> PLAC$ OV] "O DIGIT4 #CG ,*APT] #G A#G4BA ,EXAMPLE #G4AD _% #1.6: _: " _% #0.749: _: " ,QK ,REVIEW ,:5 A HORIZONTAL B> IS US$ DIRECTLY "U A S+LE DIGIT OR LR1 ! FIVE-/EP RULE IS N US$ Z EXPLA9$ 9 ,*APT] #C "<,,BANA ,NEME? ,UPDATE3 ,RULE ,,XIV1 ^S #HF;C ,3TRACT$ ,=M ( ,"UL9+ ( ,S+LE ,LETT]S_/,DIGITS1 #BJAC">4 ,WRITE ! DIRECTLY-"U 9DICATOR " & HORIZONTAL B> SYMBOL " IMMLY AF ! DIGIT OR LR4 ,TO REVIEW1 _% #72.4%: _: IS R1D Z SEV5TY-TWO PO9T F\R ) A B> "U ! #D4 ,X IS TRANSCRIB$3 _% #72.4%: _: ,S9CE X IS EXTREMELY R>E TO H A MODIFI$ EXPRES.N T USES ! DIRECTLY "U 9DICATOR "1 #CH ,*APT] #G B#G4BA ALL EX]CISE MAT]IAL W FOCUS ON MODIFI$ EXPRES.NS US+ ! DIRECTLY OV] 9DICATOR OR ! 3TRACT$ =M ( ! HORIZONTAL B> OV] A S+LE DIGIT4 -----------------------------------#G4BB ,P>ALLEL1 ,P]P5DICUL>1 ,N ,P>ALLEL1 & ,N ,P]P5DICUL> ,/UD5TS >E 9TRODUC$ TO P>ALLEL "<"S"TS CALL$ IS P>ALLEL TO"> & P]P5DICUL> "<"S"TS CALL$ IS P]P5DICUL> TO"> 9 F\R? GRADE "<,COMMON ,CORE ,/ATE ,/&>DS ,9ITIATIVE1 #BJAJ2 ,M>YL& ,DE"P;T ( ,$UCA;N1 #BJAE">4 ,X TAKES TWO CELLS TO WRITE ! ^7P>ALLEL TO SIGN^' 9 ,NEME? ,CODE4 ,X IS WRITT5 ) DOTS #A-#B-#D-#F1 FOLL[$ BY DOTS #A-#B-#C4 .=$L ,X TAKES TWO CELLS TO WRITE ! ^7P]P5DICUL> TO SIGN^' 9 ,NEME? ,CODE4 ,X IS WRITT5 ) DOTS #A-#B-#D-#F1 FOLL[$ BY DOTS #A-#B-#C-#D4 .=$P #CI ,*APT] #G A#G4BB ,/UD5TS >E 9TRODUC$ TO N P>ALLEL "<"S"TS CALL$ IS N P>ALLEL TO"> & N P]P5DICUL> "<"S"TS CALL$ IS N P]P5DICUL> TO"> 9 F\R? GRADE "<,COMMON ,CORE ,/ATE ,/&>DS ,9ITIATIVE1 #BJAJ2 ,M>YL& ,DE"P;T ( ,$UCA;N1 #BJAE">4 ,Z EXPLA9$ E>LI] 9 ? *APT]1 COMP>ISON SIGNS C 2 NEGAT$ BY PLAC+ DOTS #C-#D 2F ! SYMBOL 9 ,NEME? ,CODE4 ,X TAKES ?REE CELLS TO WRITE ! ^7N P>ALLEL TO SIGN^' 9 ,NEME? ,CODE4 ,X IS WRITT5 ) DOTS #C-#D1 FOLL[$ BY DOTS #A-#B-#D-#F1 FOLL[$ BY DOTS #A-#B-#C4 .=/$L ,X TAKES ?REE CELLS TO WRITE ! ^7N P]P5DICUL> SIGN^' 9 ,NEME? ,CODE4 ,X IS WRITT5 ) DOTS #C-#D1 FOLL[$ BY DOTS #A-#B-#D-#F1 FOLL[$ BY DOTS #A-#B-#C-#D4 .=/$P ,EXAMPLE #G4AE 3TA9S F\R EXAMPLES T %[ ! USE ( P>ALLEL1 P]P5DICUL>1 N P>ALLEL1 & N P]P5DICUL>4 #DJ ,*APT] #G #G4BC ,EXAMPLE #G4AE _% ",E,F<:] $L ",G,H<:] ",A,B<$[33O] $P ",C,D<$[33O] ",W,X<:] /$L ",Y,Z<:] ",P,Q<$O] /$P ",R,S<$O] _: ,PRACTICE #G4E ,9T]L9E ! FOLL[+ PROBLEMS T 3TA9 MODIFI$ EXPRES.NS1 P>ALLEL1 P]P5DICUL>1 N P>ALLEL1 & N P]P5DICUL>4 _% #1_4 #4."123<:] #2_4 ",A,B<$[33O] #3_4 ",R,S<$O] #4_4 #1.6: #5_4 ",E,F<$O] /$P ",E,G<$O] _: #DA ,*APT] #G A#G4BC ,USE YR BRLWRIT] TO WRITE ! FOLL[+ PROBLEMS T 3TA9 MODIFI$ EXPRES.NS1 P>ALLEL1 P]P5DICUL>1 N P>ALLEL1 & N P]P5DICUL>4 @.<,! MA? 3T5T 2L HAS BE5 SPELL$ \ TO ALL[ = PRACTICE4@.> #A4 ,IF RAY ;,,AB IS P>ALLEL TO RAY ;,,CD1 !N ! M1SURE ( ANGLE #D EQUALS ;8 #B4 ,ELEV5-OV]-TWELVE EQUALS Z]O PO9T N9E "O SIX @. OV] SIX@.> #C4 ,IF L9E ,,PQ IS P]P5DICUL> TO L9E ,,RS1 !N :AT IS ! M1SURE ( ANGLE ,,ROQ8 #D4 ,9 TRAPEZOID ,,ABCD1 L9E SEG;T ;,,AB IS N P>ALLEL TO L9E SEG;T ,,BC4 #E4 ,F\R-OV]-ELEV5 EQUALS Z]O PO9T ?REE SIX @. OV] ?REE SIX@.> -----------------------------------#G4BD ,CR1T+ ,SIMPLE ,TACTILE ,GRAPHICS ,TRIANGLES1 CIRCLES1 ANGLES1 & L9ES >E (T5 US$ 9 GEOMETRY PROBLEMS4 #DB ,*APT] #G A#G4BD ,MA!MATICAL DIAGRAMS AID ALL /UD5TS 9 "U/&+ 3CEPTS4 ,^! DIAGRAMS %D 2 PROVID$ TO BRL R1D]S Z TACTILE GRAPHICS ) BRL LABELS4 ,= EXAMPLE1 ! F/ TRIANGLE 2L 0 EASILY CR1T$ Z A BLACK L9E MA/] US+ ! ,MICROS(T ,^W ,%APES & !N LABEL$ ) ! CAPITAL PR9T LRS US+ TEXTBOXES4 ,! SECOND TRIANGLE USES ! SAME BLACK L9E MA/] & SIMPLY REPLACES ! PR9T LRS ) CAPITAL BRL LRS US+ TEXTBOXES & A BRL FONT4 ,? SAME GRAPHIC CD H AL BE5 CR1T$ US+ A BRLWRIT] & GRAPHIC >T TAPE4 #DC ,*APT] #G B#G4BD @.<,? BRL PAGE %D 2 REMOV$ & REPLAC$ ) ! PROVID$ TACTILE GRAPHIC FILE4@.> #DD ,*APT] #G C#G4BD ,DETAIL$ 9=MA;N AB H[ TO CR1TE MA!MATICAL TACTILE GRAPHICS IS AVAILABLE 9 ,UNIT #F ( ! .7,GUIDEL9ES & ,/&>DS = ,TACTILE ,GRAPHICS1 #BJAJ.'4 ,ADDI;NAL TACTILE GRAPHICS >E 9CLUD$ 9 ,"P #A ( ! ,5D ( ! ,*APT] ,EX]CISE4 ,PRACTICE CR1T+ A SIMPLE TACTILE GRAPHIC IS PROVID$ 9 ,"P #B4 ,*APT] ,SUMM>Y ,%APES _4 ,! %APE 9DICATOR IS US$ ) ! ASSIGN$ %APE SYMBOL TO REPRES5T REGUL> POLYGONS & IRREGUL> %APES4 _4 ,! ,5GLI% LR 9DICATOR IS N US$ :5 WRIT+ A %APE4 _4 ,A SPACE IS LEFT 2T ! %APE & XS ID5TIFI]1 EV5 IF "O DOES N APPE> 9 PR9T4 _4 ,:5 A REGUL> POLYGON "E"> REPRES5T+ A MISS+ SIGN ( OP]A;N IS FOLL[$ BY A NUMB]1 A MULTIPURPOSE 9DICATOR IS PLAC$ 2T ! NUM]IC #DE ,*APT] #G D#G4BD %APE SYMBOL & ! FOLL[+ NUMB]4 _4 ,:5 A %APE REPRES5TS OMITT$ MAT]IAL1 SPACE ! %APE ! SAME WAY ! OMITT$ MAT]IAL WD 2 SPAC$4 -----------------------------------#G4BE _4 ,:5 BRAILL+ ! M1SURE ( AN ANGLE1 USE 8;M0 2F ! ANGLE SYMBOL TO REPRES5T 8! M1SURE (04 ,D N USE ! ,5GLI% LR 9DICATOR OR ITALICIZE ! 8;M04 _4 ,USE ,NEME? ,CODE SWIT* 9DICATORS :5 %APES >E SURR.D$ BY TEXT4 ,SIGNS ( ,COMP>ISON ,US$ 9 ,GEOMETRY _4 ,9 GEOMETRY /UD5TS >E 9TRODUC$ TO A V>IETY ( SIGNS ( COMP>ISON S* Z 3GRU5T TO & P>ALLEL TO4 _4 ,PLACE A SPACE ON EI SIDE ( SIGNS ( COMP>ISON SYMBOLS4 ,4T.E ,2T ,TWO ,PO9TS _4 ,:5 WRIT+ ! 4T.E 2T TWO PO9TS " PLACE A CAPITAL 9DICATOR 9 FRONT ( EA* LR4 ,D N ITALICIZE ! LRS4 #DF ,*APT] #G A#G4BE ,S+LE & ,D\BLE ,PRIME ,SIGNS _4 ,! S+LE PRIME SIGN IS US$ = FEET OR M9UTES4 _4 ,! D\BLE PRIME SIGN IS US$ = 9*ES OR SECONDS4 _4 ,"! IS NO SPACE 2T ! S+LE OR D\BLE PRIME SIGN & ! QUANT;Y TO : X APPLIES4 ,TRANS=MA;NS _4 ,TRANS=MA;NS USE ! "R >R[ "<3TRACT$"> Z WELL Z ! S+LE &_/OR D\BLE PRIME SIGNS4 ,! "R >R[ IS R1D Z 8MAPS TO04 ,PI _4 ,! ,GREEK LR 9DICATOR IS US$ :5 WRIT+ ! ,GREEK LR PI4 _4 ,! LR 8;P0 FOLL[+ ! ,GREEK LR 9DICATOR IS US$ TO REPRES5T PI4 #DG ,*APT] #G B#G4BE ,MODIFI$ ^1,EXPRES.NS _4 ,COMMON SYMBOLS US$ :5 CR1T+ MODIFI$ EXPRES.NS 9CLUDE ! MULTIPURPOSE 9DICATOR1 DIRECTLY OV] 9DICATOR1 DIRECTLY "U 9DICATOR1 HORIZONTAL B>1 B>B$ >R[ AT BO? 5DS1 "R >R[ "<3TRACT$">1 & ! T]M9A;N 9DICATOR4 _4 ,! FIVE-/EP RULE IS FOLL[$ :5 WRIT+ MODIFI$ EXPRES.NS S* Z L9E1 L9E SEG;T1 RAY1 & MULTI-DIGIT REP1T+ DECIMALS4 _4 ,"! >E TWO EXCEP;NS TO ! FIVE-/EP RULE ,- "O = A S+LE DIGIT OR LR ) A HORIZONTAL B> WRITT5 DIRECTLY OV] X & ANO!R = A S+LE DIGIT OR LR ) A HORIZONTAL B> WRITT5 DIRECTLY "U X4 -----------------------------------#G4BF ,*APT] #G3 ,ANSW] ,KEY ,ANSW] #G4A #A4 ,CIRCLE ;,P #B4 ,ANGLE #A IS N EQUAL TO ANGLE ?REE #C4 ,SQU>E ,,ABCD IS SIMIL> TO SQU>E ,,EFGH #DH ,*APT] #G A#G4BF #D4 ,TRIANGLE ,,LMN IS 3GRU5T TO TRIANGLE ,,PQR _% #1_4 $C ,Q #2_4 $T ,D,E,F @: $T ,X,Y,Z #3_4 $4 ,P,Q,R,S @:.K $4 ,A,B,C,D #4_4 $[ #2 /@:.K $[ #7 _: ,ANSW] #G4B #A4 ,! M1SURE ( ANGLE ,,DEF EQUALS =TY-FIVE DEGREES #B4 SIXTY-FIVE IS GRT] ?AN OR EQUAL TO EIE@.> TWO #C4 ,! M1SURE ( ANGLE SIX M9US ! M1SURE ( ANGLE ?REE EQUALS N9ETY DEGREES #D4 SQU>E-OV]-?REE EQUALS F\R-OV]-SIX _% #1_4 M$[ ,L,M,N+M$[ ,P,Q,R .K #63^.* #2_4 #50$4"5 /.K #100$T10 #3_4 M$[ #8 .K #42^.* #4_4 ?25/5# .K ?$4/6# _: #DI ,*APT] #G B#G4BF ,ANSW] #G4C #I4 ,TRIANGLE ,,ABC IS 3GRU5T TO TRIANGLE ,,DEF4 #AJ4 ,IF ANGLE ,A & ANGLE ;,C >E COMPLE;T>Y ANGLES1 !N ! M1SURE ( ANGLE ,A PLUS ! M1SURE ( ANGLE ;,C EQUALS N9ETY DEGREES4 -----------------------------------#G4BG ,ANSW] #G4C "<3T9U$"> ,9 ! NEXT PROBLEMS1 _% $4 _: REPRES5TS A SIGN ( OP]A;N4 ,IS X _% +, -, @*, ,'OR ./ _:8 ,FILL 9 ! BOX ) ! CORRECT SIGN ( OP]A;N4 #A4 ,IF _% $[ ,P,A,Q ,'& $[ ,Q,A,R _: >E A L9E> PAIR1 !N _% M$[ ,P,A,Q$4M$[ ,Q,A,R .K #180^.* _:4 #B4 ,IF _% $[ ,P,A,Q ,'& $[ ,Q,A,R _: >E A L9E> PAIR1 !N _% #180^.*"$4M$[ ,Q,A,R .K M$[ ,P,A,Q _:4 #EJ ,*APT] #G A#G4BG ,ANSW] #G4D #A4 ;,,AB EQUALS ?IRTE5 FEET SIX 9*ES #B4 ,! M1SURE ( ANGLE F\R EQUALS =TY-FIVE DEGREES T5 M9UTES TW5TY-FIVE SECONDS #C4 ,TRIANGLE ,,XYZ "R->R[ TRIANGLE ;,X PRIME ;,Y PRIME ;,Z PRIME "R->R[ TRIANGLE ;,X D\BLE-PRIME ;,Y D\BLE-PRIME ;,Z D\BLE-PRIME @.E UNSPAC$ 9 PR9T@.> #D4 ;,C EQUALS TWO PI ;R _% #1_4 ,P,Q .K #8'2'' #2_4 $4 ,W,X,Y,Z $O $4 ,W',X',Y',Z' #3_4 M$[ ,D,E,F .K #34^.*"52'14'' #4_4 ,V .K ?1/3#.PR^2"H _: -----------------------------------#G4BH ,ANSW] #G4E #A4 F\R PO9T "O TWO ?REE @. OV] "O TWO ?REE@.> #B4 ,L9E ;,,AB #EA ,*APT] #G A#G4BH #C4 ,RAY ,,RS #D4 "O PO9T SIX @. OV] SIX@.> #E4 ,RAY ,,EF IS N P]P5DICUL> TO RAY ,,EG _% #1_4 ,',IF ",A,B<$O] $L ",C,D<$O], ,'!N M$[ #4 .K = #2_4 ?11/12# .K #0.916: #3_4 ,',IF ",P,Q<$[33O] $P ",R,S<$[33O] _: !N :AT IS _% M$[ ,R,O,Q_8 #4_4 ,',9 $G ,A,B,C,D, ",A,B<:] /$L ",B,C<:]_4 #5_4 ?4/11# .K #0."36<:] #EB