,GEOMETRY & ,TACTILE ,GRAPHICS = ,/UD5TS 9 ,GRADES #C TO #H ,LESSON #B3 ,! ,FIVE-,/EP ,RULE & ,EXCEP;NS ,,PROJECT ,,9SPIRE ,UNIV]S;Y ( ,S\? ,C>OL9A ,UP/ATE ,SLIDE #B ,OBJECTIVES ,"PICIPANTS W 2 ABLE TO3 #A4 ,R1D & WRITE MODIFI$ EXPRES.NS CR1T$ US+3 A"> ! ,FIVE-,/EP ,RULE ;B"> TWO IMPORTANT EXCEP;NS TO ! ,FIVE-,/EP ,RULE4 #B4 ,R1D & WRITE ! ,NEME? SYMBOLS = P>ALLEL1 P]P5DICUL>1 N P>ALLEL1 & N P]P5DICUL>4 #C4 ,R1D & WRITE S5T;ES #A 3TA9+ MODIFI$ EXPRES.NS4 ,SLIDE #C ,MODIFY+ ,EXPRES.NS _4 ,A MODIFI] IS DEF9$ Z A SYMBOL OR A COMB9A;N ( SYMBOLS PLAC$ DIRECTLY OV] OR "U XS RELAT$ SYMBOL OR EXPRES.N "4 _4 ,MODIFICA;N ,9DICATORS _% " _: ,MULTIPURPOSE 9DICATOR _% < _: ,DIRECTLY-OV] 9DICATOR _% % _: ,DIRECTLY-"U 9DICATOR _% ] _: ,T]M9A;N 9DICATOR #B ,SLIDE #D ,COMMON ,MODIFI]S & ,H[ TO ,R1D ,EXPRES.NS ,US+ ,!M _% : _: ,HORIZONTAL L9E ""> _% ",P,Q<:] _: ,L9E SEG;T _% ,P,Q _: @.<,HORIZONTAL B> OV] ,,PQ@.> _% #1."37<:] _: ,"O PO9T ?REE SEV5 ) ! ?REE SEV5 REP1T+ @.<,HORIZONTAL B> OV] ?REE SEV5@.> _% $[33O _: ,B>B$ >R[ AT BO? 5DS _% ",X,Y<$[33O] _: ,L9E _% ,X,Y _: @.<,B>B$ >R[ AT BO? 5DS OV] ,,XY@.> _% $O _: ,3TRACT$ "R >R[ _% ",A,B<$O] _: ,RAY _% ,A,B _: @.<,3TRACT$ "R >R[ OV] ;,,AB@.> #C ,SLIDE #E ,FIVE-,/EP ,RULE ,USE ! FIVE-/EP RULE :5 TRANSCRIB+ MODIFI$ EXPRES.NS #A4 ,MULTIPURPOSE 9DICATOR _% " _: #B4 ,EXPRES.N TO 2 MODIFI$ #C4 ,DIRECTLY-OV] 9DICATOR _% < _: OR DIRECTLY-"U 9DICATOR _% % _: #D4 ,MODIFI] ""> #E4 ,T]M9A;N 9DICATOR _% ] _: #D ,SLIDE #F ,EXAMPLES ( ,MODIFI$ ,EXPRES.NS ,US+ ! ,FIVE-,/EP ,RULE @.<,L9E SEG;T _% ,P,Q _:@.> _% ",P,Q<:] _: @.<,RAY _% ,A,B _:@.> _% ",A,B<$O] _: @.<,L9E _% ,X,Y _:@.> _% ",X,Y<$[33O] _: @.<,"O PO9T ?REE SEV51 ) ! #CG REP1T+ "<) A HORIZONTAL B>">@.> _% #1."37<:] _: @.<,F\R PO9T FIVE SEV5 TWO N9E ) ! TWO N9E REP1T+ "<) A HORIZONTAL B>">@.> _% #4.57"29<:] _: #E ,SLIDE #G ,ACTIV;Y #B,A ,TRANSCRIBE ! FOLL[+ MODIFI$ EXPRES.NS4 #C4 @.<,Z]O PO9T N9E TWO FIVE ) ! N9E TWO FIVE REP1T+ "<) A HORIZONTAL B>">@.> #D4 @.<,L9E SEG;T _% ,M,N _:@.> #E4 @.<,RAY _% ,G,H _:@.> #F4 @.<,FIVE PO9T TWO ?REE F\R SIX ) ! F\R SIX REP1T+ "<) A HORIZONTAL B>">@.> ,SLIDE #H ,ACTIV;Y #B,A3 ,ANSW] ,KEY _% #3_4 #0."925<:] #4_4 ",M,N<$[33O] #5_4 ",G,H<$O] #6_4 #5.23"46<:] _: #F ,SLIDE #I ,3TRACT$ ,=M ( ,MODIFI$ ,EXPRES.NS ,- ,EXCEP;N #A _4 ,:5 A S+LE DIGIT OR S+LE LR IS MODIFI$ ONLY BY A HORIZONTAL B> DIRECTLY OV] X1 ! SYMBOL = ! B> IS PLAC$ AF ! DIGIT OR LR4 _4 ,! FIVE-/EP RULE M/ N 2 US$4 @.<,Z]O PO9T ?REE ) ! ?REE REP1T+ "<) A HORIZONTAL B>@.> _% #0.3: _: @.<,Z]O PO9T F\R "O SIX ) ! SIX REP1T+ "<) A HORIZONTAL B>">@.> _% #0.416: _: #G ,SLIDE #AJ ,3TRACT$ ,=M ( ,MODIFI$ ,EXPRES.NS ,- ,EXCEP;N #B _4 ,:5 A S+LE DIGIT OR S+LE LR IS MODIFI$ ONLY BY A HORIZONTAL B> DIRECTLY "U X1 ! SYMBOLS = ! DIRECTLY "U 9DICATOR & ! B> >E PLAC$ AF ! DIGIT OR LR4 _4 ,! FIVE-/EP RULE M/ N 2 US$4 @.<,?REE SIX ) ! SIX "UL9$@.> _% #36%: _: @.<,F\R PO9T FIVE SEV5 ) ! FIVE "UL9$@.> _% #4.5%:7 _: @.<,N9E COMMA "O TWO EI _% #9%:,128 _: #H ,SLIDE #AA ,ACTIV;Y #B,B ,TRANSCRIBE ! FOLL[+ MODIFI$ EXPRES.NS4 #H4 @.<,Z]O PO9T SIX ) ! SIX REP1T+ "<) A HORIZONTAL B>">@.> #I4 @.<,SEV5 N9E ) ! SEV5 "UL9$@.> #AJ4 @.<,EI">@.> #AA4 @.<,F\R FIVE COMMA SIX TWO "O ) ! FIVE "UL9$@.> #I ,SLIDE #AB ,ACTIV;Y #B,B3 ,ANSW] ,KEY _% #8_4 #0.6: #9_4 #7%:9 #10_4 #8.3: #11_4 #45%:,621 _: ,SLIDE #AC ,P>ALLEL & ,P]P5DICUL> _% $L _: ,P>ALLEL "ALLEL TO"> @.<,L9E SEG;T _% ,A,B _: IS P>ALLEL TO L9E SEG;T _% ,C,D _:4@.> _% ",A,B<:] $L ",C,D<:] _: _% $P _: ,P]P5DICUL> " TO"> @.<,L9E SEG;T _% ,E,F _: IS P]P5DICUL> TO L9E SEG;T _% ,G,H _:4@.> _% ",E,F<:] $P ",G,H<:] _: #AJ ,SLIDE #AD ,N ,P>ALLEL & ,N ,P]P5DICUL> _% /$L _: ,N ,P>ALLEL "ALLEL TO"> @.<,L9E _% ,A,B _: IS N P>ALLEL TO L9E _% ,C,D _:4@.> _% ",A,B<$[33O] /$L ",C,D<$[33O] _: _% /$P _: ,N ,P]P5DICUL> " TO"> @.<,L9E _% ,E,F _: IS N P]P5DICUL> TO L9E _% ,G,H _:4@.> _% ",E,F<$[33O] /$P ",G,H<$[33O] _: #AA ,SLIDE #AE ,EXAMPLES ( ,MODIFI$ ,EXPRES.NS ,)9 ,MA!MATICAL ,S5T;ES & ,^W ,PROBLEMS @.<#A4 ,IF L9E SEG;T _% ,E,F _: IS P>ALLEL TO L9E SEG;T _% ,G,H _:1 !N ! M1SURE ( ANGLE ,A EQUALS :AT NUMB]8@.> #A4 ,IF _% ",E,F<:] $L ",G,H<:], ,'!N M$[ ,A .K = _: @.<#B4 ,SIX ELEV5?S "<) A HORIZONTAL FRAC;N B>"> EQUALS PO9T FIVE F\R ) ! FIVE F\R REP1T+ "<) A HORIZONTAL B>">4@.> #B4 _% ?6/11# .K #."54<:] _: @.<#C4 ,ID5TIFY ! VALUE ( ! "UL9$ DIGIT 9 ?REE COMMA "O TWO F\R ) ! "O "UL9$4@.> #C4 ,ID5TIFY ! VALUE ( ! "UL9$ DIGIT 9 _% #3,"%:24 _:4 #AB ,SLIDE #AF ,ACTIV;Y #B,C ,TRANSCRIBE ! FOLL[+4 #A4 @.<,RAY _% ,E,F _: IS P]P5DICUL> TO RAY _% ,E,G _:4@.> #B4 @.<,?REE-SEV5?S "<) A HORIZONTAL FRAC;N B>"> EQUALS PO9T F\R TWO EI">4@.> #C4 @.<,L9E SEG;T _% ,P,Q _: IS N P>ALLEL TO L9E SEG;T _% ,R,S _:4@.: #D4 ,ID5TIFY ! VALUE ( ! "UL9$ DIGIT 9 @. #AC ,SLIDE #AG ,ACTIV;Y #B,C3 ,ANSW] ,KEY _% #1_4 ",E,F<$O] $P ",E,G<$O] #2_4 ?3/7# .K #."428571<:] #3_4 ",P,Q<:] /$L ",R,S<:] _: ,SLIDE #AH ,ACTIV;Y #B,C3 ,ANSW] ,KEY "<,3T9U$"> #D4 ,ID5TIFY ! VALUE ( ! "UL9$ DIGIT 9 _% #6.78%:5 _:4 #AD