GSP4qQThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$ LHalf-Plane Model` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0554/Mar 2 20040#HArial Geneva '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':'88@&%>nQ\aAt[2]@&:0A>nQ\aAt[1]0AxB@@}@A?@}@?  )0w@@k@4( 4|>G@: &  nQ\aAx6( 6|>G@: &   nQ\aAy='   -# QThat document was created with a newer version of Sketchpad and cannot be opened.|This document was created with a newer version of Sketchpad. Some information may be lost. The document will open as a copy.$LCredits` a b c d e f g h i j k l m n o p q _ ,#GSP4_M_0554/Mar 2 20040#H Geneva '''$'mtr$'nme$' fj$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':'$$0>0aDB/.>Â/ h  h Lhttp://www.keypress.com/sketchpad/general_resources/advanced_sketch_gallery/0nQ\aAAdvanced Sketch Gallery <  < b!http://www.keypress.com/sketchpad2nQ\aASketchpad Resource Centerbhf$4S<0><0><0><0>>e $4T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ LlineArial Geneva nQ\aADnQ\aACnQ\aABnQ\aAA?    nQ\aAE/ nQ\aAj - nQ\aAF   -  nQ\aAG -  nQ\aAHQ C  X/#Given the boundary line, AB, constructs the hyperbolic line through two points C and D.T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LsegmentArial Geneva nQ\aADnQ\aACnQ\aABnQ\aAA?    nQ\aAE/ nQ\aAj - nQ\aAF   -  nQ\aAG -  nQ\aAHQ C   -  nQ\aAIQ CX/#Given the boundary line, AB, constructs the hyperbolic segment through points C and D.T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LrayArial Geneva nQ\aADnQ\aACraignQ\aABerblicnQ\aAA?    nQ\aAE/ nQ\aAj - nQ\aAF  @    -  nQ\aAG -  nQ\aAHQ C  - nQ\aAIQ CT/#Given the boundary line, AB, constructs the hyperbolic ray through points C and D. T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ Lparallel linesArial Geneva nQ\aAEnQ\aADnQ\aACnQ\aABnQ\aAA?    nQ\aAF/ nQ\aAj -  nQ\aAG   -  nQ\aAH -  nQ\aAIQ C   - nQ\aAJ - nQ\aAK  nQ\aAL/ nQ\aAk - nQ\aAM  - nQ\aAN - nQ\aAOQ C  nQ\aAP/ nQ\aAl - nQ\aAQ  - nQ\aAR - nQ\aASQ Cp/#Given the boundary line, AB, constructs the two hyperbolic parallel lines to a given line CD through a point E.T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ LdistanceArial Geneva  nQ\aAYnQ\aAXnQ\aABnQ\aAA?    nQ\aAC/ nQ\aAj - nQ\aAD   -  nQ\aAE -  nQ\aAFQ C   -  nQ\aAGQ C -  nQ\aAA -  nQ\aAB    $0  `t<0>nQ\aAm[1]$0  `t<0>nQ\aAm[2]$0  `t<0>nQ\aAm[3]$0  `t<0>nQ\aAm[4]0 !z `t<0> Z0&;6\_w?ĉo  ``  `` .nQ\aA=distance {3} to {4}wL/#Given the boundary line, AB, measures the hyperbolic distance from X to Y.oT{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LangleArial Geneva  nQ\aADVnQ\aACnQ\aABnQ\aAA?    nQ\aAG/ nQ\aAj -  nQ\aAH  /  nQ\aAk/  nQ\aAl -  nQ\aAE  nQ\aAI/ nQ\aAm - nQ\aAJ / nQ\aAn/ nQ\aAo - nQ\aAF)1  z<0>,nQ\aA=angle {3}-{4}-{5}yb/#Given the boundary line, AB, measures the hyperbolic angle CVD determined by the rays VC and VD.uT{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$YLparallelism angleArial Geneva  nQ\aAZnQ\aADnQ\aACnQ\aABnQ\aAA?    nQ\aAG/ nQ\aAj -  nQ\aAH   -  nQ\aAI -  nQ\aAJQ C   - nQ\aAK - nQ\aALQ C    nQ\aAM/ nQ\aAk - nQ\aAN  - nQ\aAO - nQ\aAPQ C  nQ\aAQ/ nQ\aAl - nQ\aAR  - nQ\aAS - nQ\aATQ C  @   - #"nQ\aAU - #"nQ\aAVQ C% - &nQ\aAWQ C' $/ )nQ\aAm/ *nQ\aAn - +*nQ\aAX@   - -nQ\aAY - -nQ\aAZQ C/ - 0nQ\aAA[1]Q C1 ./ 3nQ\aAo/ 4nQ\aAp - 54nQ\aAB[1],,6nQ\aAq. 7nQ\aAr/ 8nQ\aAs - 9nQ\aAC[1] : ,6 - 8<nQ\aAD[1]/ =8nQ\aAt - ;nQ\aAE[1] - ;nQ\aAF[1]Q C@? - >AnQ\aAG[1]@  : - C;nQ\aAH[1]Q CBD - EnQ\aAI[1]Q CBF   HnQ\aAJ[1]/ IHnQ\aAu - JnQ\aAK[1]   LnQ\aAL[1]/ MLnQ\aAv - NnQ\aAM[1] O/ PnQ\aAw/  QnQ\aAx - RQnQ\aAE K/ TnQ\aAy/  UnQ\aAz - VUnQ\aAF)1SW  j<0>nQ\aAm[1]0 !Xb M<0> B0&;6lm)#ĉo`DnQ\aA*= parallelism angle, line{3}{4}, point {5}rd/#Given the boundary line, AB, shows the parallelism angle determined by the line CD and the point Z.T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ Lparallelism angle, valueArial Geneva  nQ\aAEnQ\aADnQ\aACnQ\aABnQ\aAA?    nQ\aAH/ nQ\aAj -  nQ\aAI   -  nQ\aAJ -  nQ\aAKQ C     nQ\aAL/ nQ\aAk - nQ\aAM   nQ\aAN/ nQ\aAl - nQ\aAO / nQ\aAm/  nQ\aAn - nQ\aAF / nQ\aAo/  nQ\aAp - nQ\aAG)1  j<0>nQ\aAm[1]0 !b g<0> B0&;6lm)#ĉo`DnQ\aA*=parallelism angle, line {3}{4}, point {5}0f/#Given the boundary line, AB, calculates the parallelism angle determined by the line CD and point E.T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$5Langle bisectorArial Geneva nQ\aAEnQ\aADnQ\aACnQ\aABnQ\aAA?    nQ\aAF/ nQ\aAj -  nQ\aAG  @    -  nQ\aAH -  nQ\aAIQ C - nQ\aAJQ C  / nQ\aAk/ nQ\aAl - nQ\aAK  nQ\aAL/ nQ\aAm - nQ\aAM @   - nQ\aAN - nQ\aAOQ C - nQ\aAPQ C / !nQ\aAn/ "nQ\aAo - #"nQ\aAQ,$nQ\aAp. %nQ\aAq/ &nQ\aAr - 'nQ\aAR ( $ - &*nQ\aAS/ +&nQ\aAs - )nQ\aAT - )nQ\aAUQ C.- - ,/nQ\aAV@  ( - 1)nQ\aAWQ C02 - 3nQ\aAXQ C04X/#Given the boundary line, AB, constructs the angle bisector of the hyperbolic angle CDE.T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$Lperpendicular bisectorArial Geneva  nQ\aADnQ\aACnQ\aABnQ\aAA?    nQ\aAF/ nQ\aAj - nQ\aAG   -  nQ\aAH -  nQ\aAIQ C  ?   - nQ\aAE%0   `t<0>%0   `t<0>0 ! f `t<0> F0&;6l?"g#ĉo ``  nQ\aAc[1]-  nQ\aAJ - nQ\aAK - nQ\aALQ C -  nQ\aAMQ Cb/#Given the boundary line, AB, constructs the perpendicular bisector of the hyperbolic segment CD.KT{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ LmidpointArial Geneva  nQ\aADnQ\aACnQ\aABnQ\aAA?    nQ\aAF/ nQ\aAj - nQ\aAG   -  nQ\aAH -  nQ\aAIQ C  ?   - nQ\aAE%0   `t<0>%0   `t<0>0 ! f `t<0> F0&;6l?"g#ĉo ``  nQ\aAc[1]-  nQ\aAJ -  nQ\aAKQ CH/#Given the boundary line, AB, constructs the midpoint of the segment CD.T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$%Lperpendicular, exterior pointArial Geneva nQ\aAEnQ\aADnQ\aACnQ\aABnQ\aAA?    nQ\aAF/ nQ\aAj -  nQ\aAG   -  nQ\aAH -  nQ\aAIQ C     nQ\aAJ/ nQ\aAk - nQ\aAK   nQ\aAL/ nQ\aAl - nQ\aAM / nQ\aAm/  nQ\aAn - nQ\aAN / nQ\aAo/  nQ\aAp - nQ\aAO,nQ\aAq/ nQ\aAr -  nQ\aAP ! - "nQ\aAQ - "nQ\aARQ C$#z/#Given the boundary line, AB, constructs the hyperbolic perpendicular line through the point E to the hyperbolic line CD. T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$Lperpendicular, point on lineArial Geneva nQ\aADnQ\aACnQ\aABnQ\aAA?    nQ\aAE/ nQ\aAj - nQ\aAF   -  nQ\aAG -  nQ\aAHQ C    nQ\aAI  / nQ\aAk - nQ\aAJ  - nQ\aAK - nQ\aALQ C|/#Given the boundary line, AB, constructs the hyperbolic perpendicular to the hyperbolic line CD through a point on line CD.0T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$Lcircle by center radiusArial Geneva  !^  <0> >0c @ @pUnQ\aAt[1] nQ\aACo'.AnQ\aABnQ\aAA 'nQ\aAS[1]#2?  / nQ\aAj - nQ\aADB3    <0>B3    M<0>A3   4<0>0 ! r  e<0> R0 &;6 gAĉo `` ``E8 nQ\aAE%0     <0>%0    <0>0 ! b  <0> B0&;6I)*ĉo``0 ! b  <0> B0&;6`-*ĉo``0 !  b  )<0> B0&;6H'*ĉo``E8 nQ\aAF   nQ\aAG r/#Given the boundary line, AB, constructs the hyperbolic circle with center point C and radius the measurement t1. T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$Lcircle by center pointArial Geneva nQ\aADnQ\aACnQ\aABnQ\aAA?  / nQ\aAj  nQ\aAG/ nQ\aAk -  nQ\aAH   -  nQ\aAI -  nQ\aAJ?    - nQ\aAE - nQ\aAF%0    <0>%0    <0>0 ! f  -<0> F0&;6p@+O6ĉo``` nQ\aAc[1]@   - nQ\aAK  nQ\aAL Q C   -  nQ\aAMQ Ch/#Given the boundary line, AB, constructs the hyperbolic circle with center point C and radius point D. eT{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$BLcircle by 3 pointsArial Geneva nQ\aAEo.&; }@nQ\aADJ>nQ\aACnQ\aABnQ\aAA?    nQ\aAJ/ nQ\aAj -  nQ\aAK   -  nQ\aAL -  nQ\aAMQ C    nQ\aAN/ nQ\aAk - nQ\aAO  - nQ\aAP - nQ\aAQQ C?   - nQ\aAF%0    <0>%0    <0>0 ! f  <0> F0&;6l?"g#ĉo ``  nQ\aAc[1]- nQ\aAR - nQ\aAS - nQ\aATQ C?   - !nQ\aAG%0 "   <0>%0 "   <0>0 ! #$f  <0> F0&;6l?"g#ĉo ``  "%nQ\aAc[2]- &nQ\aAU - &nQ\aAV - &nQ\aAWQ C(') - * nQ\aAX/ +nQ\aAl - ,nQ\aAH%0 -+   <0>@  -+ + 0nQ\aAY/ 10nQ\aAm - 2nQ\aAZ 3+ - 4nQ\aAA[1] - 4nQ\aAB[1]?  5 - 7,nQ\aAI%0 8-   <0>0 ! .9f  <0> F0&;6p@+O6ĉo``` -:nQ\aAc[3] - /;nQ\aAC[1] <8 =nQ\aAD[1] >8Q C6+5 - 2@nQ\aAE[1]Q C+Ah/#Given the boundary line, AB, constructs, if possible, the hyperbolic circle through points C, D and E. T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$HLarcArial Geneva nQ\aAEnQ\aADnQ\aACnQ\aABnQ\aAA?    nQ\aAJ/ nQ\aAj -  nQ\aAK   -  nQ\aAL -  nQ\aAMQ C  ?   - nQ\aAF%0    <0>%0    <0>0 ! f  <0> F0&;6l?"g#ĉo ``  nQ\aAc[1]- nQ\aAN - nQ\aAO - nQ\aAPQ C  nQ\aAQ/ nQ\aAk - nQ\aAR  - nQ\aAS - nQ\aATQ C?   - !nQ\aAG%0 "   <0>%0 "   <0>0 ! #$f  <0> F0&;6l?"g#ĉo ``  "%nQ\aAc[2]- & nQ\aAU - &nQ\aAV - &nQ\aAWQ C(') - *nQ\aAX/ +nQ\aAl - ,nQ\aAH%0 -+   <0>@  -+ + 0nQ\aAY/ 10nQ\aAm - 2nQ\aAZ 3+ - 4nQ\aAA[1]?  5 - 6,nQ\aAI%0 7-   <0>0 ! .8f  <0> F0&;6p@+O6ĉo``` -9nQ\aAc[3] - /:nQ\aAB[1] ;7 <nQ\aAC[1] =7?  " - 2?nQ\aAD[1] @+@  +@ - BAnQ\aAE[1]Q C+C - ?DnQ\aAF[1]Q C+E - >FnQ\aAG[1]Q CGt/#Given the boundary line, AB, constructs, if possible, a hyperbolic arc which passes through the points C, D and E.T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$7 LequidistantArial Geneva  nQ\aADnQ\aAC !^  <0> >0c @ @pUnQ\aAt[2] nQ\aAAnQ\aAB'nQ\aAS[1]?  / nQ\aAj - nQ\aAG   nQ\aAH/  nQ\aAk -  nQ\aAI   - nQ\aAJ - nQ\aAKQ C - nQ\aAL   - nQ\aAM/ nQ\aAl - nQ\aAEB3   2<0>B3   2<0>A3   2<0>%0   2<0>0 !r 2<0> R0 &;6 gAĉo `` ``E8nQ\aAF%0   2<0>0 ! b 2<0> B0&;6I)*ĉo``0 ! b 2<0> B0&;6`-*ĉo``0 ! b 2<0> B0&;6H'*ĉo``E8 nQ\aAN ! "nQ\aAO #! - $nQ\aAP- $nQ\aAQ?  &?  % - 'nQ\aAR - 'nQ\aAS * ) ,nQ\aAT/ -,nQ\aAm +nQ\aAU/ /+nQ\aAn - 0.nQ\aAV 1 - 2nQ\aAW - 2nQ\aAXQ C4*3 - (nQ\aAYQ C463z/#Given the boundary line, AB, constructs the hyperbolic equidistant to the line CD at a distance given by Measurement t2.T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$" LhorocycleArial Geneva  nQ\aADnQ\aACnQ\aABnQ\aAA?  / nQ\aAj - nQ\aAF%0   `t<0>@     nQ\aAG/  nQ\aAk -  nQ\aAH   - nQ\aAI - nQ\aAJ?   - nQ\aAE%0   `t<0>0 ! f `t<0> F0&;6p@+O6ĉo``` nQ\aAc[1] -  nQ\aAK  nQ\aAL Q C -  nQ\aAMQ C. nQ\aAl  nQ\aAN/ nQ\aAm -  nQ\aAO !v/#Given the boundary line, AB, constructs the horocycles obtained by the circle with center point C and radius point D.T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$$ LtriangleArial Geneva nQ\aAEnQ\aADnQ\aACnQ\aABnQ\aAA?    nQ\aAF/ nQ\aAj -  nQ\aAG   -  nQ\aAH -  nQ\aAIQ C   -  nQ\aAJQ C  nQ\aAK/ nQ\aAk - nQ\aAL  - nQ\aAM - nQ\aANQ C - nQ\aAOQ C  nQ\aAP/ nQ\aAl - nQ\aAQ  - nQ\aAR - nQ\aASQ C ! - "nQ\aATQ C#Z/#Given the boundary line, AB, construct the hyperbolic triangle with vertices C, D and E. T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$@Ltriangle areaArial Geneva nQ\aAEpt@nQ\aADu@`p@nQ\aACC.+@@nQ\aAB16m@1p@nQ\aAA?    nQ\aAG/ nQ\aAj -  nQ\aAH   -  nQ\aAI -  nQ\aAJQ C   -  nQ\aAKQ C  nQ\aAL/ nQ\aAk - nQ\aAM  - nQ\aAN - nQ\aAOQ C - nQ\aAPQ C  nQ\aAQ/ nQ\aAl - nQ\aAR  - nQ\aAS - nQ\aATQ C ! - "nQ\aAUQ C# / %nQ\aAm/ &nQ\aAn - &'nQ\aAA  / )nQ\aAo/ *nQ\aAp - +*nQ\aAB  / -nQ\aAq/ .nQ\aAr - ./nQ\aAC / 1nQ\aAs/ 2nQ\aAt - 32nQ\aAD / 5nQ\aAu/ 6nQ\aAv - 67nQ\aAE / 9nQ\aAw/ :nQ\aAx - ;:nQ\aAF)1(,   <0>$nQ\aA angle E-C-D)104   <0>$nQ\aA angle C-D-E)18<   -<0>$nQ\aA angle D-E-C0 !=>?n /J<0> N0  wwղw> #```nQ\aAm[1] L/#Given the boundary line, AB, measures the area of hyperbolic triangle, CDE.T{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$uLsegment transportArial Geneva nQ\aAEP@b@nQ\aAC'pp@b@nQ\aADf@P@nQ\aAC0t@O@nQ\aABo@ P@nQ\aAA__o@b@?    nQ\aAO/  nQ\aAj -  nQ\aAP   -  nQ\aAQ -  nQ\aARQ C  -  nQ\aASQ C  nQ\aAT/ nQ\aAk - nQ\aAU @   - nQ\aAV - nQ\aAWQ C - nQ\aAXQ C  nQ\aAY/ nQ\aAl - nQ\aAZ   - !nQ\aAA[1] - !nQ\aAB[1]Q C"#?   - %nQ\aAF%0 &   <0>%0 &   <0>0 ! '(f  <0> F0&;6l?"g#ĉo ``  &)nQ\aAc[1]- *$nQ\aAG - *nQ\aAH - *nQ\aAIQ C,+- - .nQ\aAC[1] - .nQ\aAD[1] /0 1nQ\aAJ@  2%0 2  <0>.0.   <0>0 ! 54f :<0> F0&;6f ĉo``` 26nQ\aAc[2] - 37nQ\aAK 8 9nQ\aAE[1]/ :9nQ\aAm - ;nQ\aAF[1] <8@  < - >=nQ\aAG[1] <?/ @nQ\aAn/ 8AnQ\aAo - BAnQ\aAH[1] - nQ\aAI[1]Q CD / FnQ\aAp/ GnQ\aAq - HGnQ\aAJ[1],CInQ\aAr. JnQ\aAs/ KnQ\aAt - LnQ\aAK[1] M CI - KOnQ\aAL[1]/ PKnQ\aAu - NnQ\aAM[1] - NnQ\aAN[1]Q CSR - QTnQ\aAL@  M - VNnQ\aAO[1]Q CUW - XnQ\aAMQ CUY - ZnQ\aAP[1] [ \nQ\aAQ[1]/ ]\nQ\aAv - ^nQ\aAN%0 _8  <0>.0Z  <0>0 ! a`f <0> F0&;6eĉo``` _bnQ\aAc[3]@  _8 - dcnQ\aAR[1]   - fnQ\aAS[1] - fnQ\aAT[1]Q Cgh -  inQ\aAU[1]Q Cj e lnQ\aAV[1]/ mlnQ\aAw - nnQ\aAW[1] oe - pnQ\aAX[1] - pnQ\aAY[1]Q Cqer - nsnQ\aAZ[1]Q Cet/#Given the boundary line, AB, transports the hyperbolic segment CD to another hyperbolic segment with an end point C' and direction C'E.