GSP4QThat 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.$xLHalf-Plane Model` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0534/Jun 30 20030#` Arial '''$'$'$'$'$'$'$'$'$'$' $' $' %'&'8'8'8'9':' A@R@@@B @@? @ )@P~@`t@4(@ 4\.B@: &@  nQ\aAx6(n 6\.B@: &n  nQ\aAy='n  %0n    <0>0 3n j  <0> J0sww-wL &``n  n nQ\aAA[1])1n    <0>^D>nQ\aAt[1]^DnHFn)3>>nQ\aAt[2]n)9=-# i{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$!LLine Arial  nQ\aADG2nQ\aAChl,[,nQ\aABQ,P@,X,nQ\aAAm,j,'nQ\aAS[1]?    nQ\aAD/n nQ\aAj -n  nQ\aAAA3n    <0>A3n    5<0>/n nQ\aAk -n  nQ\aAB@ n nQ\aAl0 !n  n  e<0># N0 VAGAG} `` "nQ\aA m[1]=m[1])1n   }<0>   - nQ\aAE -n nQ\aAFQ Cn%0     <0>0 ! d  <0> D0sww-w`` ?   - nQ\aAC)1n  <0>@  nQ\aAm%0n   .<0>0 !nj B<0># J0sww-w\``0 !n | l<0>? \0VAGAG}   `` "nQ\aA m[3] D0$sww-w\$"`` n X/#Given the boundary line, AB, constructs the hyperbolic line through two points C and D.i{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$)LSegment Arial  nQ\aADp,z@@nQ\aACB@Ѕ@@nQ\aABPwЅ@@nQ\aAA'nQ\aAS[1]8+y+0+?   nQ\aAn nnQ\aAD/n nQ\aAjA3n    <0>A3n    <0>0 !n  n  5<0># N0 VAGAG} `` "nQ\aA m[1]=m[1]/n nQ\aAk -n  nQ\aAA)1n   M<0>0 !  d  a<0> D0sww-w((`` -  nQ\aABn  -n nQ\aAE -n nQ\aAFQ Cn -  nQ\aAGQ Cn/ nQ\aAl -n nQ\aAHn nQ\aAmn%0    y<0>0 !j  <0># J0sww-wL &``?   -  nQ\aAC)1n!   <0>@  !0 !"`  <0>e,ef @0sww-w '`!$%0    <0>0 ! &|  <0> \0VAGAG}   `` "nQ\aA m[2] B0sww-w "``n%!(X/#Given the boundary line, AB, constructs the hyperbolic segment through points C and D.i{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.$4LRay Arial  nQ\aAD@@nQ\aACp@@nQ\aABnQ\aAA'nQ\aAS[1]?    nQ\aAE/n nQ\aAj -n  nQ\aAAn  @ n   -n  nQ\aAF -n  nQ\aAGQ Cn - nQ\aAHQ Cn/ nQ\aAk -n nQ\aAB)1n   <0>A3    <0>A3    <0>0 ! n  <0># N0 VAGAG} `` "nQ\aA m[1]=m[2]nB3    =<0>B3    U<0>0 ! |  m<0>? \0VAGAG}   `` "nQ\aA m[3] H0sww-w("```0 !p  <0># P0 sww-w@#`` `  nQ\aAln/ nQ\aAm -n  nQ\aAC)1n!   <0>!"@  #nQ\aAn n$%0   <0>0 !&j <0> J0 sww-w   ``%0    <0>0 ! '(| <0> \0VAGAG}   `` "nQ\aA m[6]0 !,)h 3<0># H0 sww-w  $```+,+,@  ./nQ\aAo n0+- .+nQ\aAp0 !n,)p  <0> P0 sww-w $`` ` 2+3/#Given the boundary line, AB, constructs the hyperbolic ray through points C and D. Given the boundary line, AB, constructs the hyperbolic ray through points C and D. i{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$nLParallel lines Arial  nQ\aAEp@@nQ\aADnQ\aACN1 1nQ\aABnQ\aAAPp1'nQ\aAS[1]?  %0    <0>0 !j  <0># J0sww-w\``A3    <0>   nQ\aAI/n  nQ\aAj -n  nQ\aAAA3n    <0>/n nQ\aAk -n nQ\aAB@ n nQ\aAl0 !n  n  <0> N0 VAGAG} `` "nQ\aA m[1]=m[1])1n   <0>  - nQ\aAJ -n nQ\aAKQ Cn%0    <0>0 ! d  <0># D0sww-w`` ?   - nQ\aAC)1n   <0>@  nQ\aAm0 !n  |  <0>? \0VAGAG}   `` "nQ\aA m[3] D0$sww-w\$"`` n! - nQ\aAD -n nQ\aAEn $ n%nQ\aAL/n &%nQ\aAn -n 'nQ\aAFn ( -n )nQ\aAM -n )nQ\aANQ Cn$+Q C*$%0 $(  W<0>%0   W<0>0 !/j W-<0># J0sww-w,``@  $nQ\aAp/n nQ\aAo -n 2nQ\aAG)1n3  X<0>)1$  Wl<0>A3 $  X<0>A3   X<0>0 ! 67n X<0> N0 VAGAG} `` "nQ\aA m[2]=m[2]0 !n 48d X<0># D0sww-w%`` n1$90 ! 0.| YU<0> \0VAGAG}   `` "nQ\aA m[1] D0sww-w,`` n1$< # >nQ\aAO/n ?>nQ\aAq -n @nQ\aAH%0n #A  ><0>0 !n 0B| R<0>? \0VAGAG}   `` "nQ\aA m[1]0 !n D7n <0># N0 VAGAG} `` "nQ\aA m[5]=m[2]0 !n 4Ed <0> D0sww-w&``@ n #nQ\aAr)1n#  h<0>0 ! HCd ~<0># D0sww-w$`` G#I A - KnQ\aAP -n KnQ\aAQQ Cn#MQ CL# G#F - "nQ\aAR&0n "  (<0>0 !nRb (<0> B0sww-w ``n Q nTnQ\aAS/n UTnQ\aAs -n VnQ\aATn W -n XnQ\aAU -n XnQ\aAVQ CnQZQ CYQA3   (-<0>A3   (E<0>0 !^]Rn (]<0># N0 sww-w~$ `` ` "_S - nQ\aAWn a nbnQ\aAX/n cbnQ\aAt -n dnQ\aAYn e -n fnQ\aAZ -n fnQ\aAA[1]mQ CnahQ Cga&0   (u<0>0 !^]kj (<0> J0sww-w~ `` `0 !kb (<0># B0sww-w~$`` lmp/#Given the boundary line, AB, constructs the two hyperbolic parallel lines to a given line CD through a point E.i{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.$$ LDistance Arial  nQ\aADu@@nQ\aACnQ\aABnQ\aAA'nQ\aAS[1]?    nQ\aAF/n nQ\aAj -n  nQ\aAA/n nQ\aAkn   -n  nQ\aAB -n  nQ\aACn  n  n n $0n   W<0>nQ\aAm[3]$0n   m<0>nQ\aAm[5]$0n   <0>nQ\aAm[4]$0n   <0>nQ\aAm[6]0 !nz <0> Z0sww-w~%  ``  `` ,nQ\aA= distance {4}-{5} A3n   <0>A3n   <0>0 !n n 9<0> N0 VAGAG} `` "nQ\aA m[1]=m[1] -n  nQ\aAD)1n  Q<0>0 ! d e<0># D0sww-w~*`` nQ\aAln -  nQ\aAE%0n !  }<0>nQ\aAm[7]m%0n !  <0>nQ\aAm[8]m0 !n "#j <0> J0sww-w~!  `` ,nQ\aA= distance {4}-{5} L/#Given the boundary line, AB, measures the hyperbolic distance from C to D.oi{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$<LAngle Arial  EDCnQ\aAB:@P@@nQ\aAA@P@'@nQ\aAS[1]s@@y@? @ @  @nQ\aAJ/n  nQ\aAj -n  nQ\aAKn  /n  nQ\aAk/n  nQ\aAl -n  nQ\aAAn  nnQ\aAL/n nQ\aAm -n nQ\aAMn /n nQ\aAn/n nQ\aAo -n nQ\aAB)1n  <0>,nQ\aA= angle {4}-{5}-{6}A3n   <0>A3n   <0>A3n   <0>0 !n n <0># N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n n <0> N0 VAGAG} `` "nQ\aA m[2]=m[1]/n nQ\aAp -n nQ\aACn nQ\aAq)1n  <0> !0 ! !d 3<0># D0sww-w~'``"# - $nQ\aAD.n nQ\aArn % -n '&nQ\aAE)1n(  <0>,nQ\aA= angle {4}-{5}-{6}n %.n nQ\aAs -n *+nQ\aAF)1n,  <0>,nQ\aA= angle {4}-{5}-{6}/n nQ\aAt -n .nQ\aAGn /nQ\aAu)1n/  <0>0 ! 1d /<0> D0 sww-w~ #``0/13/2 - 4nQ\aANn 5 -n &6nQ\aAH)1n7  G<0>,nQ\aA= angle {4}-{5}-{6}n 5.n nQ\aAv -n 9:nQ\aAI)1n;  [<0>,nQ\aA= angle {4}-{5}-{6}b/#Given the boundary line, AB, measures the hyperbolic angle CDE determined by the rays DC and DE.ui{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LParallelism angle, line Arial  lnQ\aAE@ +nQ\aAD3.ؖnQ\aACXnQ\aAB.nQ\aAA'nQ\aAS[1]2,?  nQ\aAk[1]n  nnQ\aAX/n  nQ\aAj -n  nQ\aAAn   -n  nQ\aAY -n  nQ\aAZQ Cn  - nQ\aAB -n nQ\aACQ Cn   nQ\aAA[1]/n nQ\aAk -n nQ\aAB[1]n  -n nQ\aAC[1] -n nQ\aAD[1]Q Cn  nQ\aAE[1]/n nQ\aAl -n nQ\aADn  -n nQ\aAF[1] -n nQ\aAG[1]Q Cn ! @   - $#nQ\aAH[1] -n $#nQ\aAI[1]Q Cn& - 'nQ\aAJ[1]Q Cn( %/ *nQ\aAm/n +nQ\aAn -n ,+nQ\aAK[1]@ n  -n .nQ\aAL[1] -n .nQ\aAM[1]Q Cn0 - 1nQ\aAN[1]Q Cn2 // 4nQ\aAo/n 5nQ\aAp -n 65nQ\aAO[1],n-7nQ\aAq.n 8nQ\aAr/n 9nQ\aAs -n :nQ\aAEn ;n -7 -n 9=nQ\aAP[1]/n >9nQ\aAt -n <nQ\aAQ[1] -n <nQ\aAR[1]Q CnA@ - ?BnQ\aAS[1]@ n ; -n D<nQ\aAT[1]Q CnCE - FnQ\aAU[1]Q CnCG  InQ\aAV[1]/n JInQ\aAu -n KnQ\aAW[1]n   nMnQ\aAX[1]/n NMnQ\aAv -n OnQ\aAY[1]n P/n QnQ\aAw/n  RnQ\aAx -n SRnQ\aAFn L/n UnQ\aAy/n VnQ\aAz -n WVnQ\aAG)1nTX   <0>0 !Yb <0># B0&;6lm)#ĉo`<nQ\aA# parallelism angle, lineCD, point E%0n    <0>0 !n[j  <0> J0sww-w\``A3n    <0>A3n    <0>/n nQ\aAa -n _nQ\aAH@ n `nQ\aAb0 !n ]^n  <0># N0 VAGAG} `` "nQ\aA m[1]=m[1])1n`   <0>   - dnQ\aAZ[1]m -n dnQ\aAA[2]mQ Cnef%0  `   <0>0 ! cbd  <0> D0sww-w`` a`i?   - knQ\aAI)1nl   <0>@  lnQ\aAc0 !n \h|  <0>? \0VAGAG}   `` "nQ\aA m[3]# D0$sww-w\$"`` nnlp - gnQ\aAJ -n gnQ\aAK@ n snQ\aAfA3n s   <0>A3n r   <0>@ n rnQ\aAh -n qnQ\aAB[2]m -n jnQ\aAC[2]mn s nznQ\aAD[2]m/n {znQ\aAd -n |nQ\aALn } -n ~nQ\aAE[2]m -n ~nQ\aAF[2]mQ CnsQ Cs%0 s}   <0>/ nQ\aAe -n nQ\aAM)1n   <0>)1s   <0>A3    <0>0 ! un  <0> N0 VAGAG} `` "nQ\aA m[2]=m[2]0 !n d  <0># D0sww-w%`` nts0 ! \|  <0> \0VAGAG}   `` "nQ\aA m[1] D0sww-w,`` nts r nQ\aAG[2]m/n nQ\aAg -n nQ\aAN%0n r   <0>0 !n \|  <0>? \0VAGAG}   `` "nQ\aA m[1]# N0 VAGAG} `` "nQ\aA m[5]=m[2]0 !n d  <0> D0sww-w&``)1nr   <0>0 ! d  <0># D0sww-w$`` wr  - nQ\aAH[2]m -n nQ\aAI[2]mQ CnrQ Cr wr&0 q   <0>0 !b  <0> B0sww-w `` x nQ\aAJ[2]m/n nQ\aAi -n nQ\aAK[2]mn  -n nQ\aAL[2]m -n nQ\aAM[2]mQ CnxQ Cx0 !]n  <0># N0 sww-w~$ `` ` q y nQ\aAN[2]m/n nQ\aAj[1]m -n nQ\aAO[2]mn  -n nQ\aAP[2]m -n nQ\aAQ[2]mQ CnyQ Cy&0 j   <0>0 !]j  <0> J0sww-w~ `` `0 !b  <0># B0sww-w~$`` j%0 ;   <0>%0    -<0>0 !j  A<0> J0sww-w'``0 ! ~  k<0> ^0VAGAG}    `` "nQ\aA m[1]>m[1]n  nnQ\aAO)1n   <0>0 ! b  <0># B0sww-w%``  - nQ\aAR[2]m)1n   <0>B3    <0> nQ\aAm[1]mn  nnQ\aAS[2]m/n nQ\aAl[1]m -n nQ\aAPn @ n  -n nQ\aAT[2]m -n nQ\aAU[2]mQ Cn - nQ\aAV[2]mQ CnA3    <0>0 ! n  <0> N0 VAGAG} `` "nQ\aA m[1]=m[2]B3n    <0>0 !n |  <0>? \0VAGAG}   `` "nQ\aA m[3]# H0sww-w("```0 !p  <0> P0 sww-w@#`` ` / nQ\aAn[1]m -n nQ\aAQ)1n   <0>@  nQ\aAo[1]m n%0    <0>0 ! \|  <0> \0VAGAG}   `` "nQ\aA m[6]0 !h  <0># H0 sww-w  $```@  nQ\aAp[1]m n nQ\aAq[1]m0 !np  <0> P0 sww-w $`` `   nQ\aAS)1n   <0>nQ\aAm[2]m/n nQ\aAr[1]m -n nQ\aAT@ n nQ\aAs[1]m0 !n ^]n  <0># N0 VAGAG} `` "nQ\aA m[1]=m[1])1n   <0>%0    <0>0 ! d  <0> D0sww-w`` )1l   <0>0 ! \|  <0>? \0VAGAG}   `` "nQ\aA m[3]# D0$sww-w\$"`` nnl@  nQ\aAt[1]mA3n    <0>A3n    <0>@ n nQ\aAu[1]m -n nQ\aAW[2]m -n nQ\aAX[2]m%0n    <0>)1n   <0>0 ! n  <0> N0 VAGAG} `` "nQ\aA m[2]=m[2]0 !n d  <0># D0sww-w%`` n0 ! \|  <0> \0VAGAG}   `` "nQ\aA m[1] D0sww-w,`` n0 ! n  <0># N0 VAGAG} `` "nQ\aA m[5]=m[2]0 !n  d  <0> D0sww-w&`` n    nQ\aAY[2]m/n  nQ\aAv[1]m -n nQ\aAZ[2]mn  -n nQ\aAA[3]mQ Cn  nQ\aAB[3]m/n nQ\aAw[1]m -n nQ\aAC[3]mn  -n nQ\aAD[3]m -n nQ\aAE[3]mQ CnQ C&0    <0>0 !^j  <0># J0sww-w~ `` `0 !b  <0> B0sww-w~$``  - nQ\aAF[3]m -n nQ\aAG[3]mn !" n#nQ\aAH[3]m? n $/n %nQ\aAx[1]m -n nQ\aAI[3]m -n nQ\aAJ[3]mn '( n)nQ\aAK[3]m? n */n +nQ\aAy[1]m -n &nQ\aAU -n  nQ\aAV)1n-.   -<0>0 ! /n  -<0># N0 sww-w$  ` ` <nQ\aA#parallelism angle, line CD, point E -n ,nQ\aAW)1n1.   A<0>nQ\aAm[3]l0 !n 2r  A<0>? R0  sww-w #  `  ` <nQ\aA#parallelism angle, line CD, point E -n nQ\aAL[3]l -n nQ\aAM[3]ln 45 n6nQ\aAN[3]l? n 7/n 8nQ\aAz[1]l -n j9nQ\aAO[3]l -n nQ\aAP[3]l.n nQ\aAa[1]l"n ;<,n:=nQ\aAb[1]l/n >nQ\aAc[1]l -n ?nQ\aAQ[3]ln @ -n jAnQ\aAR[3]l -n ?AnQ\aAS[3]l -n ?AnQ\aAT[3]lQ CnCBD - EnQ\aAU[3]lQ CnCBF - nQ\aAV[3]l -n nQ\aAW[3]ln HI nJnQ\aAX[3]l? n K/n LnQ\aAd[1]l -n MqnQ\aAY[3]l -n nQ\aAZ[3]l/n nQ\aAe[1]l"n OP,nNQnQ\aAf[1]l/n RnQ\aAg[1]l -n SnQ\aAA[4]ln T -n SUnQ\aAB[4]l -n SUnQ\aAC[4]l -n qUnQ\aAD[4]lQ CnVXW - YnQ\aAE[4]lQ CnVXZ - nQ\aAF[4]l -n nQ\aAG[4]ln \] n^nQ\aAH[4]l? n _/n `nQ\aAh[1]l -n ajnQ\aAI[4]l/n nQ\aAi[1]l"n ;c,nbdnQ\aAj[2]l/n enQ\aAk[2]l -n fnQ\aAJ[4]ln g -n fhnQ\aAK[4]l -n fhnQ\aAL[4]l -n jhnQ\aAM[4]lQ Cnjki - lnQ\aAN[4]lQ Cnjkm - nQ\aAO[4]l -n nQ\aAP[4]ln op nqnQ\aAQ[4]l? n r/n snQ\aAl[2]l -n tqnQ\aAR[4]l,nuQnQ\aAm[2]l/n vnQ\aAn[2]l -n wnQ\aAS[4]ln x -n wynQ\aAT[4]l -n wynQ\aAU[4]l -n qynQ\aAV[4]lQ Cn{|z - }nQ\aAW[4]lQ Cn|~d/#Given the boundary line, AB, shows the parallelism angle determined by the line CD and the point E.i{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.$dLParallelism angle, value Arial  lnQ\aAEnQ\aAD(wnQ\aACu@unQ\aABnQ\aAA'nQ\aAS[1]?  A3    <0>   nQ\aAM/n  nQ\aAj -n  nQ\aAAA3n    <0>/n nQ\aAk -n nQ\aAB@ n nQ\aAl0 !n  n  <0> N0 VAGAG} `` "nQ\aA m[1]=m[1])1n   <0>   - nQ\aAN -n nQ\aAOQ Cn0 ! d  <0># D0sww-w`` ?   - nQ\aAC@ n  -n nQ\aAD -n nQ\aAE@ n nQ\aAnA3n    <0>A3n    <0>@ n nQ\aAo -n nQ\aAP/n nQ\aAm -n #nQ\aAF)1n$   <0>A3    <0>0 ! &n  <0> N0 VAGAG} `` "nQ\aA m[2]=m[2]0 !n %'d  <0># D0sww-w%`` n(0 !  &n  <0> N0 VAGAG} `` "nQ\aA m[5]=m[2]0 !n %*d  <0># D0sww-w&`` n!+ " -nQ\aAQ/n .-nQ\aAp -n /nQ\aARn 0 -n 1nQ\aAS -n 1nQ\aATQ Cn"3Q C2"&0    <0>0 !&6j  <0> J0sww-w~ `` `0 !6b  <0># B0sww-w~$`` 78   - :nQ\aAU -n :nQ\aAVn < n=nQ\aAW/n >=nQ\aAq -n ?nQ\aAXn ; nAnQ\aAY/n BAnQ\aAr -n CnQ\aAZn D/n EnQ\aAs/n ;FnQ\aAt -n GFnQ\aAGn @/n InQ\aAu/n <JnQ\aAv -n KJnQ\aAH)1nHL   <0>0 !Mb  <0> B0&;6lm)#ĉo`<nQ\aA#parallelism angle, line CD, point E -n 4nQ\aAA[1]l -n 4nQ\aAB[1]ln OP nQnQ\aAC[1]l? n R/n SnQ\aAw -n 5nQ\aAD[1]l -n 5nQ\aAE[1]ln UV nWnQ\aAF[1]l? n X/n YnQ\aAx -n TnQ\aAI -n 9nQ\aAJ)1n[\  `<0>  ^nQ\aAK)1n_  a$<0>0 ! `]n  <0># N0 sww-w$  ` ` <nQ\aA#parallelism angle, line CD, point E -n ZnQ\aAL)1nb\   <0>0 ! `cr  <0> R0  sww-w #  `  ` nQ\aAm[1]lf/#Given the boundary line, AB, calculates the parallelism angle determined by the line CD and point E.ai{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.$LAngle Bisector Arial  nQ\aAE8@@nQ\aADB@@nQ\aAC`q@@@nQ\aAB))nQ\aAA)3&'nQ\aAS[1],b,,?  nQ\aAdn  nnQ\aAT/n  nQ\aAj -n  nQ\aAAn  @ n   -n  nQ\aAU -n  nQ\aAVQ Cn - nQ\aAWQ Cn  / nQ\aAk/n nQ\aAl -n nQ\aAXn  nnQ\aAY/n nQ\aAm -n nQ\aABn @ n  -n nQ\aAZ -n nQ\aAA[1]Q Cn - nQ\aAB[1]Q Cn  / "nQ\aAn/n #nQ\aAo -n $#nQ\aAC[1],n%nQ\aAp.n &nQ\aAq/n 'nQ\aAr -n (nQ\aACn )n % -n '+nQ\aAD[1]/n ,'nQ\aAs -n *nQ\aAE[1] -n *nQ\aAF[1]Q Cn/. - -0nQ\aAG[1]@ n ) -n 2*nQ\aAH[1]Q Cn13 - 4nQ\aAI[1]Q Cn15%0    <0>0 !7j  <0> J0 sww-w   ``/ nQ\aAt -n 9nQ\aAD)1n:   <0>A3    <0>:;B3    <0> :=nQ\aAun   -n  @nQ\aAJ[1]Q CnA - BnQ\aAK[1]Q CnCA3    <0>0 ! <En  <0># N0 VAGAG} `` "nQ\aA m[1]=m[2]B3n    <0>0 !n >G|  <0>? \0VAGAG}   `` "nQ\aA m[3] H0sww-w("```0 !;FHp  <0># P0 sww-w@#`` ` ?:J/ nQ\aAv -n LnQ\aAE)1nM   <0>MN@  =OnQ\aAw nP:I%0  :   <0>0 ! 8R|  <0> \0VAGAG}   `` "nQ\aA m[6]0 !VSHh  <0> H0 sww-w  $```UVUV@  XYnQ\aAx nZUW XUnQ\aAy0 !nVSHp  <0># P0 sww-w $`` ` \U] - nQ\aAL[1]mQ Cn_A3    <0>0 ! <an  <0> N0 VAGAG} `` "nQ\aA m[1]=m[2]B3n    <0>0 !n >c|  <0>? \0VAGAG}   `` "nQ\aA m[3]# H0sww-w("```0 !;bdp  <0> P0 sww-w@#`` ` ?:f/ nQ\aAz -n hnQ\aAG)1ni   <0>ij@  =knQ\aAa nl:e%0 :   <0>0 ! 8n|  <0> \0VAGAG}   `` "nQ\aA m[6]0 !rodh  <0># H0 sww-w  $```qrqr@  tunQ\aAb nvqs tqnQ\aAc0 !nrodp  <0> P0 sww-w $`` ` xqy)1:   <0>A3    <0>A3    1<0>B3    I<0>B3    a<0>0 ! |}n  y<0># N0 VAGAG} `` "nQ\aA m[1]=m[2]0 !n ~~  <0>? ^0VAGAG}    `` "nQ\aA m[3]>m[3]0 !n{f  <0> F0 sww-w "``` : - !nQ\aAI)1n   <0>0 !f  <0># F0sww-w```  - nQ\aAM[1]mn  -n nQ\aAN[1]m -n nQ\aAO[1]mn  -n nQ\aAP[1]mQ Cn - nQ\aAQ[1]mA3n    <0>B3n    <0>0 !n }n  <0> N0 VAGAG} `` "nQ\aA m[4]=m[2]0 !n ~  2<0> ^0VAGAG}    `` "nQ\aA m[4]>m[3]0 !n{f G<0># F0sww-w"``` : - nQ\aAJ)1n   b<0>0 !f  v<0> F0sww-w ```  - nQ\aAR[1]mn  -n nQ\aAS[1]m -n nQ\aAT[1]m -n nQ\aAU[1]mQ Cn - nQ\aAV[1]mQ Cn - gnQ\aAK -n nQ\aAL)1n   <0>0 !`  <0> @0sww-w$`@  nQ\aAe n)1   <0>0 ! f  <0># F0 sww-w '`` / nQ\aAf -n nQ\aAW[1]mn  -n nQ\aAX[1]m -n nQ\aAY[1]m -n nQ\aAZ[1]mQ Cn - nQ\aAA[2]mQ Cn - KnQ\aAM -n !nQ\aAN@ n nQ\aAg)1n   <0>0 !`  <0>e,ef @0sww-w,` )1   <0>0 ! f  <0> F0sww-w%`` / nQ\aAh -n nQ\aAB[2]mn  -n nQ\aAC[2]m -n nQ\aAD[2]m -n nQ\aAE[2]mQ Cn - nQ\aAF[2]mQ CnQ C%0 :)  <0>%0   <0>0 !j <0># J0sww-w>$``0 ! ~ <0>? ^0VAGAG}    `` "nQ\aA m[4]>m[4])1n:  '<0>0 ! b ;<0> B0 sww-w> #`` : nQ\aAG[2]m/n nQ\aAi -n nQ\aAO@ n inQ\aAj[1]m0 !n Ean S<0># N0 VAGAG} `` "nQ\aA m[1]=m[1])1ni  S<0>  - nQ\aAH[2]m -n nQ\aAI[2]mQ Cn%0 i  S<0>0 ! d S<0> D0sww-w`` i?   - nQ\aAP)1n  S<0>@  nQ\aAk[1]m0 !n 8| S<0> \0VAGAG}   `` "nQ\aA m[3]# D0$sww-w\$"`` n - nQ\aAJ[2]mn  nnQ\aAK[2]m/n nQ\aAl[1]m -n nQ\aAQn @ n  -n nQ\aAL[2]m -n nQ\aAM[2]mQ Cn - nQ\aAN[2]mQ CnA3   S<0>0 ! <n S<0> N0 VAGAG} `` "nQ\aA m[1]=m[2]B3n   S<0>0 !n >| S<0>? \0VAGAG}   `` "nQ\aA m[3]# H0sww-w("```0 !;p S<0> P0 sww-w@#`` ` ?:/ nQ\aAm[1]m -n nQ\aAR)1n  S<0>@  =nQ\aAn[1]m n:%0 :  S<0>0 ! 8| S<0> \0VAGAG}   `` "nQ\aA m[6]0 !h S<0># H0 sww-w  $```@  nQ\aAo[1]m n nQ\aAp[1]m0 !np S<0> P0 sww-w $`` ` X/#Given the boundary line, AB, constructs the angle bisector of the hyperbolic angle CDE.i{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LLPerpendicular bisector Arial  inQ\aADv@@nQ\aACnQ\aABnQ\aAA'nQ\aAS[1]?   nQ\aAn nnQ\aAA/n nQ\aAj -n  nQ\aABn   -n  nQ\aAF -n  nQ\aAGQ Cn  ?   - nQ\aAC%0n    <0>%0n    <0>0 !n f  <0># F0&;6l?"g#ĉo `` n nQ\aAc[1]-n nQ\aAH -n nQ\aAI -n nQ\aAJQ Cn -  nQ\aAKQ Cn%0    <0>0 !j  <0> J0sww-wL &``A3    <0>/ nQ\aAk -n nQ\aAD)1n   <0> A3    <0>0 ! "n  <0># N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n  #d  <0> D0sww-w((``n / %nQ\aAl -n &nQ\aALn !'nQ\aAmn($)1   <0>@  0 !*`  <0> @0sww-w '`,%0    <0>0 ! .|  .<0>? \0VAGAG}   `` "nQ\aA m[2]# B0sww-w "``n-0B3    <0>B3    <0>0 ! 23n  5<0> N0 VAGAG} `` "nQ\aA m[1]=m[1]/n nQ\aAo -n 5nQ\aAE)1n6   M<0>0 ! 74b  a<0># B0 sww-w #``%0 6   y<0>%0    <0>0 !:j  <0> J0sww-w(``0 ! 9;~  <0> ^0VAGAG}    `` "nQ\aA m[3]>m[2]@ n 6nQ\aAp n=68)1    <0>0 ! ?<b  <0># B0sww-w)``@   nQ\aAq nA @%0    F<0>%0    Z<0>0 ! DCf  n<0> F0sww-w$ ``  EnQ\aAc[2]m -n 1FnQ\aAM -n FnQ\aAN -n FnQ\aAOQ CnHGI - )FnQ\aAPQ CnHKIb/#Given the boundary line, AB, constructs the perpendicular bisector of the hyperbolic segment CD. i{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.$Q LMidpoint Arial  nQ\aADnQ\aACn nQ\aAB nQ\aAA 'nQ\aAS[1] ?   nQ\aAn nnQ\aAA/n nQ\aAj -n  nQ\aABn   -n  nQ\aAF -n  nQ\aAGQ Cn  ?   - nQ\aAC%0n    <0>%0n    <0>0 !n f  <0># F0&;6l?"g#ĉo `` n nQ\aAc[1]-n nQ\aAH -n nQ\aAI -n nQ\aAJQ Cn -  nQ\aAKQ Cn%0    <0>0 !j  <0> J0sww-wL &``A3    <0>/ nQ\aAk -n nQ\aAD)1n   <0> A3    <0>0 ! "n  <0># N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n  #d  <0> D0sww-w((``n / %nQ\aAl -n &nQ\aALn !'nQ\aAmn($)1   <0>@  0 !*`  <0>e,ef @0sww-w '`,%0    <0>0 ! .|  .<0>? \0VAGAG}   `` "nQ\aA m[2]# B0sww-w "``n-0B3    <0>B3    <0>0 ! 23n  5<0> N0 VAGAG} `` "nQ\aA m[1]=m[1]/n nQ\aAo -n 5nQ\aAE)1n6   M<0>0 ! 74b  a<0># B0 sww-w #``%0 6   y<0>%0    <0>0 !:j  <0> J0sww-w(``0 ! 9;~  <0> ^0VAGAG}    `` "nQ\aA m[3]>m[2]@ n 6nQ\aAp n=68 - >nQ\aAM)1n    <0>0 ! @<b  <0># B0sww-w)``@   nQ\aAq nB A%0    F<0>%0    Z<0>0 ! EDf  n<0> F0sww-w$ ``  FnQ\aAc[2]m -n 1GnQ\aAN -n GnQ\aAO -n GnQ\aAPQ CnIHJ - )GnQ\aAQQ CnILJ - )MnQ\aAR -n 1KnQ\aAS-n nQ\aAT -n CnQ\aAUH/#Given the boundary line, AB, constructs the midpoint of the segment CD.i{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.$LPerpendicular exterior point Arial  xnQ\aAE@v@@nQ\aADHnQ\aAC0nQ\aABx@nQ\aAA'nQ\aAS[1]?  %0    <0>0 !j  <0># J0sww-w\``A3    <0>   nQ\aAI/n  nQ\aAj -n  nQ\aAAA3n    <0>/n nQ\aAk -n nQ\aAB@ n nQ\aAl0 !n  n  <0> N0 VAGAG} `` "nQ\aA m[1]=m[1])1n   <0>  - nQ\aAJ -n nQ\aAKQ Cn%0    <0>0 ! d  <0># D0sww-w`` ?   - nQ\aAC)1n   <0>@  nQ\aAm0 !n  |  <0>? \0VAGAG}   `` "nQ\aA m[3] D0$sww-w\$"`` n! - nQ\aAD -n nQ\aAE@ n $nQ\aAoA3n $   <0>A3n #   <0>@ n #nQ\aAp -n nQ\aAL/n nQ\aAn -n *nQ\aAF)1n+   <0>A3    <0>0 ! &-n  <0># N0 VAGAG} `` "nQ\aA m[2]=m[2]0 !n ,.d  <0> D0sww-w%`` n%$/0 ! '-n  <0># N0 VAGAG} `` "nQ\aA m[5]=m[2]0 !n ,1d  <0> D0sww-w&`` n(#2 ) 4nQ\aAM/n 54nQ\aAq -n 6nQ\aANn 7 -n 8nQ\aAO -n 8nQ\aAPQ Cn):Q C9)&0    <0>0 !- =j  <0># J0sww-w~ `` `0 !=b  <0> B0sww-w~$`` >?Q C  BnQ\aAQ/n CBnQ\aAr -n DnQ\aARn  nFnQ\aAS/n GFnQ\aAs -n HnQ\aATn I/n JnQ\aAt/n KnQ\aAu -n LKnQ\aAUn E/n NnQ\aAv/n OnQ\aAw -n POnQ\aAV,nMQnQ\aAx/n RnQ\aAy -n SnQ\aAGn T -n UnQ\aAW -n UnQ\aAXQ CnWV - ;nQ\aAY -n ;nQ\aAZn YZ n[nQ\aAA[1]m? n \/n ]nQ\aAz -n ^nQ\aAB[1]m -n @nQ\aAC[1]m.n nQ\aAa"n `a,n_bnQ\aAb/n cnQ\aAc -n dnQ\aAD[1]mn e -n fnQ\aAE[1]m -n fnQ\aAF[1]mQ Cngh - <nQ\aAG[1]m -n <nQ\aAH[1]mn jk nlnQ\aAI[1]m? n m/n nnQ\aAd -n onQ\aAJ[1]m,nbpnQ\aAe/n qnQ\aAf -n rnQ\aAK[1]mn s -n tnQ\aAL[1]m -n tnQ\aAM[1]mQ Cnuv%0 +T  <0>%0   <0>0 !yj 1<0># J0sww-w#`` #$ {nQ\aAH)1n|  s<0>)1+  <0>@  +nQ\aAg0 !n xz~ [<0> ^0VAGAG}    `` "nQ\aA m[3]>m[2]0 !n~}p <0> P0 sww-w% `  ` ` |v/#Given the boundary line, AB, constructs the hyperbolic perpendicular line through the point E to hyperbolic line CD.i{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.$ALPerpendicular point line Arial  onQ\aADy@@nQ\aACnLB68@@@nQ\aABV@p@@nQ\aAAHrr@@'@nQ\aAS[1]ݹuv@p@? @ %0@    <0>0 !@j  <0># J0sww-w\``A3@    <0>@  @ nQ\aAH/n  nQ\aAj -n  nQ\aAAA3n    <0>/n nQ\aAk -n nQ\aAB@ n nQ\aAl0 !n  n  <0> N0 VAGAG} `` "nQ\aA m[1]=m[1])1n   <0>   - nQ\aAI -n nQ\aAJQ Cn%0     <0>0 ! d  <0># D0sww-w`` ?   - nQ\aAC)1n   <0>@  nQ\aAm0 !n |  <0>? \0VAGAG}   `` "nQ\aA m[3] D0$sww-w\$"`` n    - "nQ\aAK -n "nQ\aALQ Cn#$ %nQ\aADn  &/n &'nQ\aAn -n (nQ\aAEn )& -n *nQ\aAM -n *nQ\aANQ Cn,&+/ &nQ\aAo -n .nQ\aAF%0n /)   <0>%0n    <0>0 !n1j  -<0># J0sww-w$``0 !n 02~  W<0> ^0VAGAG}    `` "nQ\aA m[1]>m[1] -n nQ\aAO -n nQ\aAPn 45 n6nQ\aAG)1n7&   o<0>@  7nQ\aAp0 !n 83b  <0> B0sww-w(`` n97: nQ\aAQ -n nQ\aARn =< -n >nQ\aAS -n >nQ\aATQ Cn?<@v/#Given the boundary line, AB, constructs the hyperbolic perpendicular line through the point E to hyperbolic line CD.i{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LCircle by center radius Arial  !r^  <0> >0c @ @pUnQ\aAt[1] nnQ\aACo'.AAnQ\aABnQ\aAA 'nQ\aAS[1]#2?  / nQ\aAj -n nQ\aADB3n    <0>B3n    M<0>A3n   4<0>0 !n r  e<0>? R0 &;6 gAĉo `` ``E8 nQ\aAE%0n     <0>%0n    <0>0 !n b  <0># B0&;6I)*ĉo``0 !n b  <0> B0&;6`-*ĉo``0 !n  b  )<0># B0&;6H'*ĉo``E8n nQ\aAFn   nnQ\aAGn r/#Given the boundary line, AB, constructs the hyperbolic circle with center point C and radius the measurement t1.Ci{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.$BLCircle by center point Arial  rnQ\aAD^@@nQ\aACx-&nQ\aAB-&nQ\aAA&?,-'nQ\aAS[1]?  / nQ\aAj -n nQ\aAA%0n    <0>@ n %0n    <0>0 !n j  <0> J0sww-wL &``A3n    <0>)1n   <0>/ nQ\aAk -n nQ\aAEn nQ\aAlA3n    <0>0 !n  n  <0># N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n d  <0> D0sww-w((``n?   - nQ\aAB@ n )1n   <0>0 !`  <0>e,ef @0sww-w '` nQ\aAmn nQ\aAF/n nQ\aAn -n  nQ\aAC%0n !   <0>0 !n  "|  <0> \0VAGAG}   `` "nQ\aA m[2]# B0sww-w "``n$ ! - &nQ\aAG -n &nQ\aAHQ Cn'( -  )nQ\aAIQ Cn*Q C(' -  ,nQ\aAJQ Cn-?  ( - /nQ\aAD%0n 0   <0>0 !n  1f  <0> F0&;6p@+O6ĉo```n 2nQ\aAc[1]m -n  3nQ\aAKn 40 n5nQ\aALn 60%0n    <0>%0n    <0>A3n    W<0>A3n    o<0>0 !n ;:n  <0># N0 VAGAG} `` "nQ\aA m[3]=m[3]0 !n9<8j  -<0> J0sww-w```` =nQ\aAc[2]m -n  >nQ\aAMn ? n@nQ\aANn A?h/#Given the boundary line, AB, constructs the hyperbolic circle with center point C and radius point D. ei{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.$BLCircle by 3 points Arial nnQ\aAEo.&; }@@nQ\aADJ>nQ\aACnQ\aABnQ\aAA?    nQ\aAJ/n nQ\aAj -n  nQ\aAKn   -n  nQ\aAL -n  nQ\aAMQ Cn    nQ\aAN/n nQ\aAk -n nQ\aAOn  -n nQ\aAP -n nQ\aAQQ Cn?   - nQ\aAF%0n    <0>%0n    <0>0 !n f  <0># F0&;6l?"g#ĉo `` n nQ\aAc[1]-n nQ\aAR -n nQ\aAS -n nQ\aATQ Cn?   - !nQ\aAG%0n "   <0>%0n "   <0>0 !n #$f  <0> F0&;6l?"g#ĉo `` n "%nQ\aAc[2]-n &nQ\aAU -n &nQ\aAV -n &nQ\aAWQ Cn(') - * nQ\aAX/n +nQ\aAl -n ,nQ\aAH%0n -+   <0>@ n -+n + n0nQ\aAY/n 10nQ\aAm -n 2nQ\aAZn 3+ -n 4nQ\aAA[1] -n 4nQ\aAB[1]? n 5 -n 7,nQ\aAI%0n 8-   <0>0 !n .9f  <0># F0&;6p@+O6ĉo```n -:nQ\aAc[3] -n /;nQ\aAC[1]n <8 n=nQ\aAD[1]n >8Q Cn6+5 - 2@nQ\aAE[1]Q Cn+Ah/#Given the boundary line, AB, constructs, if possible, the hyperbolic circle through points C, D and E. i{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.$HLArc Arial nQ\aAEnQ\aADnQ\aACnQ\aABnQ\aAA?    nQ\aAJ/n nQ\aAj -n  nQ\aAKn   -n  nQ\aAL -n  nQ\aAMQ Cn  ?   - nQ\aAF%0n    <0>%0n    <0>0 !n f  <0> F0&;6l?"g#ĉo `` n nQ\aAc[1]-n nQ\aAN -n nQ\aAO -n nQ\aAPQ Cn  nQ\aAQ/n nQ\aAk -n nQ\aARn  -n nQ\aAS -n nQ\aATQ Cn?   - !nQ\aAG%0n "   <0>%0n "   <0>0 !n #$f  <0># F0&;6l?"g#ĉo `` n "%nQ\aAc[2]-n & nQ\aAU -n &nQ\aAV -n &nQ\aAWQ Cn(') - *nQ\aAX/n +nQ\aAl -n ,nQ\aAH%0n -+   <0>@ n -+n + n0nQ\aAY/n 10nQ\aAm -n 2nQ\aAZn 3+ -n 4nQ\aAA[1]? n 5 -n 6,nQ\aAI%0n 7-   <0>0 !n .8f  <0> F0&;6p@+O6ĉo```n -9nQ\aAc[3] -n /:nQ\aAB[1]n ;7 n<nQ\aAC[1]n =7? n " -n 2?nQ\aAD[1]n @+@ n +@ -n BAnQ\aAE[1]Q Cn+C - ?DnQ\aAF[1]Q Cn+E - >FnQ\aAG[1]Q CnGt/#Given the boundary line, AB, constructs, if possible, a hyperbolic arc which passes through the points C, D and E..i{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.$d LEquidistant Arial   !^  <0> >0ޟ|@<,|@@pUnQ\aAt[1] nnQ\aAD@q@@nQ\aACnQ\aABnQ\aAA'nQ\aAS[1]?  %0    <0>0 !j  <0># J0sww-w\``A3    <0>   nQ\aAF/n  nQ\aAj -n  nQ\aAAA3n    <0>/n nQ\aAk -n nQ\aAB@ n nQ\aAl0 !n  n  <0> N0 VAGAG} `` "nQ\aA m[1]=m[1])1n   <0>  - nQ\aAG -n nQ\aAHQ Cn%0    <0>0 ! d  <0># D0sww-w`` ?   - nQ\aAC)1n   <0>@  nQ\aAm0 !n  |  <0>? \0VAGAG}   `` "nQ\aA m[3] D0$sww-w\$"`` n!  - #nQ\aAI -n #nQ\aAJQ Cn$% - &nQ\aAK -n &nQ\aALn '( n)nQ\aAMn '*-n &+nQ\aAN/n ,nQ\aAn -n -nQ\aADA3n ,   <0>B3n ,   <0>B3n .   <0>n .,0 !n01r  <0> R0 sww-w& `` ``E8/3nQ\aAO0 !n01r  <0>? R0 sww-w%` `` `E8/5nQ\aAPn 64 n7nQ\aAQn 84 -n 92nQ\aAR-n 92nQ\aAS@ n .;@ n .: -n <+nQ\aATQ Cn'>( - =+nQ\aAUQ Cn'@(/ nQ\aAo -n BnQ\aAEB3n    <0>B3n C   <0>0 !nDEr  <0> R0 sww-w& `` ``E8 FnQ\aAV0 !nDEr  <0>? R0 sww-w%` `` `E8 HnQ\aAWn IG nJnQ\aAXn KG -n "nQ\aAY -n "LnQ\aAZ -n "LnQ\aAA[1]mn NO nPnQ\aAB[1]mn QM nRnQ\aAC[1]mn SQ -n LTnQ\aAD[1]m-n LTnQ\aAE[1]m@ n MV@ n MU -n nQ\aAF[1]m -n LnQ\aAG[1]m -n LnQ\aAH[1]mn Z[ n\nQ\aAI[1]mn Y] n^nQ\aAJ[1]mn _] -n L`nQ\aAK[1]m-n L`nQ\aAL[1]m@ n Yb@ n Yaz/#Given the boundary line, AB, constructs the hyperbolic equidistant to the line CD at a distance given by Measurement t1.i{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$" LHorocycle Arial  nQ\aADnQ\aACnQ\aABnQ\aAA?  / nQ\aAj -n nQ\aAF%0n   `t<0>@ n n  n nQ\aAG/n  nQ\aAk -n  nQ\aAHn   -n nQ\aAI -n nQ\aAJ? n  -n nQ\aAE%0n   `t<0>0 !n f `t<0># F0&;6p@+O6ĉo```n nQ\aAc[1] -n  nQ\aAKn  nnQ\aALn Q Cn -  nQ\aAMQ Cn. nQ\aAln  nnQ\aAN/n nQ\aAm -n  nQ\aAOn !v/#Given the boundary line, AB, constructs the horocycles obtained by the circle with center point C and radius point D.i{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.$i LTriangle Arial  nQ\aAE@y@@nQ\aAD.@H@@nQ\aACrH@@nQ\aAB'm@h@@nQ\aAAA9Ɂ@h@'@nQ\aAS[1]Z@h@? @ %0@    <0>0 !@j  <0> J0sww-wL &``A3@    <0>/@ nQ\aAj -n  nQ\aAF)1n    <0>  nQ\aAn nnQ\aAO/n nQ\aAkA3n    <0>0 !n  n  <0># N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n  d  <0> D0sww-w((`` -n nQ\aAGn  -n nQ\aAP -n nQ\aAQQ Cn - nQ\aARQ Cn / nQ\aAl -n nQ\aASn nQ\aAmn ?   - !nQ\aAH)1n"   <0>@  "0 !#`  <0>e,ef @0sww-w '`"%%0     <0>0 !  '|  <0> \0VAGAG}   `` "nQ\aA m[2]# B0sww-w "``n&")/ nQ\aAo -n +nQ\aAI)1n,   <0>,- nQ\aAs n/nQ\aAT/n 0/nQ\aApA3n    <0>0 !n 2n  <0> N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n -3d  <0># D0sww-w((`` -n 1nQ\aAJn 5 -n 6nQ\aAU -n 6nQ\aAVQ Cn87 - 19nQ\aAWQ Cn:,-/ <nQ\aAq -n =nQ\aAXn .>nQ\aArn?,4?   - AnQ\aAK)1nB   <0>@  B0 !C`  <0> @0sww-w '`/BE%0 ,5   <0>0 !  G|  <0>? \0VAGAG}   `` "nQ\aA m[2] B0sww-w "``nFBI/ nQ\aAt -n KnQ\aAL)1nL   <0>LM nQ\aAx nOnQ\aAY/n POnQ\aAu0 !n 2 n  <0># N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n MRd  <0> D0sww-w((`` -n QnQ\aAMn T -n UnQ\aAZ -n UnQ\aAA[1]mQ CnWV - QXnQ\aAB[1]mQ CnYLM/ [nQ\aAv -n \nQ\aAC[1]mn N]nQ\aAwn^LS?   - `nQ\aAN)1na   <0>@  a0 !b`  <0>e,ef @0sww-w '`Oad%0 LT   <0>0 !  f|  <0> \0VAGAG}   `` "nQ\aA m[2]# B0sww-w "``neahZ/#Given the boundary line, AB, construct the hyperbolic triangle with vertices C, D and E. i{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$LTriangle area Arial  nQ\aAE{@@nQ\aAD@@@nQ\aACA>nQ\aABnQ\aAA'nQ\aAS[1]?  %0    <0>0 !j  <0> J0sww-wL &``A3    <0>/ nQ\aAj -n  nQ\aAA)1n    <0>  nQ\aAn nnQ\aAE[1]/n nQ\aAkA3n    <0>0 !n  n  <0># N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n  d  <0> D0sww-w((`` -n nQ\aABn  -n nQ\aAF[1]m -n nQ\aAG[1]mQ Cn - nQ\aAH[1]mQ Cn / nQ\aAl -n nQ\aAI[1]mn nQ\aAmn ?   - !nQ\aAC)1n"   <0>@  "0 !#`  <0> @0sww-w '`"%%0     <0>0 !  '|  <0>? \0VAGAG}   `` "nQ\aA m[2]# B0sww-w "``n&")/ nQ\aAo -n +nQ\aAD)1n,   <0>,- nQ\aAs n/nQ\aAJ[1]m/n 0/nQ\aApA3n    <0>0 !n 2n  <0> N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n -3d  <0># D0sww-w((`` -n 1nQ\aAEn 5 -n 6nQ\aAK[1]m -n 6nQ\aAL[1]mQ Cn87 - 19nQ\aAM[1]mQ Cn:,-/ <nQ\aAq -n =nQ\aAN[1]mn .>nQ\aArn?,4?   - AnQ\aAF)1nB   <0>@  B0 !C`  <0>e,ef @0sww-w '`/BE%0 ,5   <0>0 !  G|  <0> \0VAGAG}   `` "nQ\aA m[2] B0sww-w "``nFBI/ nQ\aAt -n KnQ\aAG)1nL   <0>LM nQ\aAx nOnQ\aAO[1]m/n POnQ\aAu0 !n 2 n  <0># N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n MRd  <0> D0sww-w((`` -n QnQ\aAHn T -n UnQ\aAP[1]m -n UnQ\aAQ[1]mQ CnWV - QXnQ\aAR[1]mQ CnYLM/ [nQ\aAv -n \nQ\aAS[1]mn N]nQ\aAwn^LS?   - `nQ\aAI)1na   <0>@  a0 !b`  <0> @0sww-w '`Oad%0 LT   <0>0 !  f|  <0>? \0VAGAG}   `` "nQ\aA m[2]# B0sww-w "``neah  nQ\aAy)1n    <0>j k. nQ\aAzn /n nnQ\aAa/n onQ\aAb -n opnQ\aAJ0 !n kd  <0> D0sww-w~'``nl r - snQ\aAK.n nQ\aAcn t -n vunQ\aALn t -n xmnQ\aAMn 5/n znQ\aAd/n {nQ\aAe -n |{nQ\aAN)1nq}  <0>&nQ\aA angle Q-R-Qt0 !n 2n  <0># N0 VAGAG} `` "nQ\aA m[2]=m[1])1nw}   <0>&nQ\aA angle Q-R-Qt)1ny}   -<0>&nQ\aA angle Q-R-Qtn LnQ\aAf)1nL   A<0>0 ! d  A<0> D0 sww-w~ #``LL - nQ\aAT[1]en  -n unQ\aAO)1nq  C<0>&nQ\aA angle Q-R-Qtn .n nQ\aAg -n nQ\aAP)1nq   U<0>&nQ\aA angle Q-R-Qtn ,nQ\aAh)1n,   i<0>, 5/ nQ\aAi/n nQ\aAj[1]e -n nQ\aAQ0 !n 3d  i<0># D0sww-w~'``n, - nQ\aARn  -n nQ\aASn  -n unQ\aATn T/n nQ\aAk[1]e/n nQ\aAl[1]e -n nQ\aAU)1n   i<0>&nQ\aA angle R-Q-Qt0 !n  2n  }<0> N0 VAGAG} `` "nQ\aA m[2]=m[1])1n   }<0>&nQ\aA angle R-Q-Qt)1n   <0>&nQ\aA angle R-Q-Qt0 !n kd  <0># D0 sww-w~ #``nl  - nQ\aAU[1]en  -n nQ\aAV)1n   <0>&nQ\aA angle R-Q-Qtn  -n mnQ\aAW)1n   <0>&nQ\aA angle R-Q-Qtn T/n nQ\aAm[1]e/n nQ\aAn[1]e -n nQ\aAX0 !n Rd  <0> D0sww-w~'``nL - nQ\aAYn  -n mnQ\aAZn  -n nQ\aAA[1]en /n nQ\aAo[1]e/n nQ\aAp[1]e -n nQ\aAB[1]e)1n   <0>&nQ\aA angle Q-Q-Rt0 !n  n  <0># N0 VAGAG} `` "nQ\aA m[2]=m[1])1n   <0>&nQ\aA angle Q-Q-Rt)1n   <0>&nQ\aA angle Q-Q-Rt0 !n d  <0> D0 sww-w~ #``n, - nQ\aAV[1]en  -n mnQ\aAC[1]e)1n   <0>&nQ\aA angle Q-Q-Rtn  -n unQ\aAD[1]e)1n   <0>&nQ\aA angle Q-Q-Rt0 !n~z  1<0> Z0sww-w~( `  `  ` ,nQ\aA= area {4}-{5}-{6}h0 !n~z  I<0>? Z0sww-w~! `  `  ` ,nQ\aA= area {4}-{5}-{6}h0 !n~z  a<0> Z0sww-w~  `  `  ` ,nQ\aA= area {4}-{5}-{6}h0 !nz  y<0>? Z0sww-w~& `  `  ` ,nQ\aA= area {4}-{5}-{6}h0 !nz  <0> Z0sww-w~" `  `  ` ,nQ\aA= area {4}-{5}-{6}h0 !nz  <0>? Z0sww-w~& `  `  ` ,nQ\aA= area {4}-{5}-{6}h0 !nz  <0> Z0sww-w~ `  `  ` ,nQ\aA= area {4}-{5}-{6}hL/#Given the boundary line, AB, measures the area of hyperbolic triangle, CDE.i{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.$LSegment transport Arial  rnQ\aADp@@q@@nQ\aACq@`f@@nQ\aALf0 !@ j  <0># J0sww-wL &``A3@    <0>/@ nQ\aAj -n  nQ\aAE)1n    <0>  nQ\aAn nnQ\aAM[1]/n nQ\aAkA3n    <0>0 !n  n  <0> N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n d  <0># D0sww-w((`` -n nQ\aAFn  -n nQ\aAG -n nQ\aAHQ Cn - nQ\aAN[1]mQ Cn / nQ\aAl -n nQ\aAO[1]mn nQ\aAmn ?   - "nQ\aAI)1n#   <0>@  #0 !$`  <0>e,ef @0sww-w '`#&%0     <0>0 !  (|  <0>? \0VAGAG}   `` "nQ\aA m[2] B0sww-w "``n'#*/ nQ\aAo -n ,nQ\aAJ)1n-   <0>A3    <0>-.B3    <0> -0nQ\aAqn  n3nQ\aAP[1]m/n 43nQ\aAp -n 5nQ\aAKn 6@ n 6 -n 87nQ\aAQ[1]m -n 87nQ\aAR[1]mQ Cn: - ;nQ\aAS[1]mQ Cn<A3    <0>0 ! />n  <0># N0 VAGAG} `` "nQ\aA m[1]=m[2]B3n    <0>0 !n 1@|  <0> \0VAGAG}   `` "nQ\aA m[3] H0sww-w("```0 !.?Ap  <0># P0 sww-w@#`` ` 2-C/ nQ\aAr -n EnQ\aAL)1nF   <0>FG@  0HnQ\aAs nI-B%0 6-   <0>0 !  K|  <0>? \0VAGAG}   `` "nQ\aA m[6]0 !OLAh  <0> H0 sww-w  $```NONO@  QRnQ\aAt nSNP QNnQ\aAu0 !nOLAp  <0># P0 sww-w $`` ` UNV)1    <0>  nQ\aAvnY X    $0[   <0>$0\   <0>$0]   <0>$0^   <0>0 !_a`bz  <0> Z0sww-w~%  ``  `` &nQ\aA distance M-L0 !n Xd  <0> D0sww-w~*``nZ d - enQ\aAN%0n f   <0>%0n f   <0>0 !n ghj  <0># J0sww-w~!  `` &nQ\aA distance M-LB3n -   -<0>A3n -   -<0>%0n -   -<0>0 !n1jcr  -<0>? R0 &;6 gAĉo `` ``E8kmnQ\aAO%0n n-   -<0>0 !n lob  -<0> B0&;6I)*ĉo``0 !n lpb  -<0># B0&;6`-*ĉo``0 !n qjb  -<0> B0&;6H'*ĉo``E8nkrnQ\aAT[1]an ns ntnQ\aAU[1]an us-n =vnQ\aAV[1]aA3n 9   -<0>/n 9nQ\aAw -n ynQ\aAP)1nz9   -<0>9z{ 9wnQ\aAa n}nQ\aAW[1]a/n ~}nQ\aAxA3n w   -<0>0 !n xn  -<0># N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n {d  -<0> D0sww-w((`` -n nQ\aAQn 9 -n nQ\aAX[1]m -n nQ\aAY[1]mQ Cn9 - nQ\aAZ[1]mQ Cn9wwz{/ nQ\aAy -n nQ\aAA[2]mn |nQ\aAznz?  w9 - nQ\aAR)1n9   -<0>@  0 !`  -<0> @0sww-w '`}%0 z   -<0>0 !  |  -<0> \0VAGAG}   `` "nQ\aA m[2]# B0sww-w "``nB3 9   -<0>B3 z   -<0>A3 z   -<0>%0 9z   -<0>0 !ir  -<0>? R0 &;6 gAĉo `` ``E8nQ\aAS%0n z   -<0>0 !n b  -<0> B0&;6I)*ĉo``0 !n b  -<0># B0&;6`-*ĉo``0 !n b  -<0> B0&;6H'*ĉo``E8nnQ\aAB[2]mn  nnQ\aAC[2]mn -n =nQ\aAD[2]mn 9nQ\aAe nnQ\aAE[2]m/n nQ\aAbA3n    -<0>0 !n xn  -<0># N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n {d  -<0> D0sww-w((`` -n nQ\aATn 9 -n nQ\aAF[2]m -n nQ\aAG[2]mQ Cn9 - nQ\aAH[2]mQ Cn9z{/ nQ\aAc -n nQ\aAI[2]mn |nQ\aAdnz?  9 - nQ\aAU)1n9   -<0>@  0 !`  -<0>e,ef @0sww-w '`%0 z   -<0>0 !  |  -<0> \0VAGAG}   `` "nQ\aA m[2]# B0sww-w "``n - WnQ\aAJ[2]mn nQ\aAi nnQ\aAK[2]m/n nQ\aAfA3n    -<0>0 !n /n  -<0> N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n .d  -<0># D0sww-w((`` -n nQ\aAVn  -n nQ\aAL[2]m -n nQ\aAM[2]mQ Cn - nQ\aAN[2]mQ Cn-./ nQ\aAg -n nQ\aAO[2]mn 0nQ\aAhn-?   - nQ\aAW)1n   -<0>@  0 !`  -<0> @0sww-w '`%0 -   -<0>0 !  |  -<0>? \0VAGAG}   `` "nQ\aA m[2] B0sww-w "``n0 !1jir  -<0> R0 &;6 gAĉo `` ``E8knQ\aAX%0n -   -<0>0 !n lb  -<0># B0&;6I)*ĉo``0 !n lb  -<0> B0&;6`-*ĉo``0 !n jb  -<0># B0&;6H'*ĉo``E8nknQ\aAP[2]mn  nnQ\aAQ[2]mn  -n DnQ\aAR[2]mn nQ\aAm[1]m nnQ\aAS[2]m/n nQ\aAj[1]mA3n    -<0>0 !n /n  -<0> N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n .d  -<0># D0sww-w((`` -n nQ\aAYn  -n nQ\aAT[2]m -n nQ\aAU[2]mQ Cn - nQ\aAV[2]mQ Cn-./ nQ\aAk[1]m -n nQ\aAW[2]mn 0nQ\aAl[1]mn-?   - nQ\aAZ)1n   -<0>@  0 !`  -<0>e,ef @0sww-w '`%0 -   -<0>0 !  |  -<0>? \0VAGAG}   `` "nQ\aA m[2] B0sww-w "``n - TnQ\aAX[2]mn 9 n nQ\aAY[2]m/n   nQ\aAn[1]m -n  nQ\aAZ[2]mn  9 -n  nQ\aAA[3]m -n  nQ\aAB[3]mQ Cn9 -  nQ\aAC[3]mQ Cn9 nQ\aAr[1]m nnQ\aAD[3]m/n nQ\aAo[1]mA3n    -<0>0 !n /n  -<0># N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n .d  -<0> D0sww-w((`` -n nQ\aAA[1]mn  -n nQ\aAE[3]m -n nQ\aAF[3]mQ Cn - nQ\aAG[3]mQ Cn-./  nQ\aAp[1]m -n !nQ\aAH[3]mn 0"nQ\aAq[1]mn#-?   - %nQ\aAB[1]m)1n&   -<0>@  &0 !'`  -<0> @0sww-w '`&)%0 -   -<0>0 !  +|  -<0> \0VAGAG}   `` "nQ\aA m[2]# B0sww-w "``n*&- - JnQ\aAI[3]mn /nQ\aAv[1]m n0nQ\aAJ[3]m/n 10nQ\aAs[1]mA3n /   -<0>0 !n /3n  -<0> N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n .4d  -<0># D0sww-w((`` -n 2nQ\aAC[1]mn 6 -n 7nQ\aAK[3]m -n 7nQ\aAL[3]mQ Cn98 - 2:nQ\aAM[3]mQ Cn;//-./ =nQ\aAt[1]m -n >nQ\aAN[3]mn 0?nQ\aAu[1]mn@-5?  / - BnQ\aAD[1]m)1nC   -<0>@  C0 !D`  -<0>e,ef @0sww-w '`0CF%0 -6   -<0>0 !  H|  -<0>? \0VAGAG}   `` "nQ\aA m[2] B0sww-w "``nGCJ - TvnQ\aAO[3]mn LnQ\aAz[1]m nMnQ\aAP[3]m/n NMnQ\aAw[1]mA3n L   -<0>0 !n /Pn  -<0># N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n .Qd  -<0> D0sww-w((`` -n OnQ\aAE[1]mn S -n TnQ\aAQ[3]m -n TnQ\aAR[3]mQ CnVU - OWnQ\aAS[3]mQ CnXLL-./ ZnQ\aAx[1]m -n [nQ\aAT[3]mn 0\nQ\aAy[1]mn]-R?  L - _nQ\aAF[1]m)1n`   -<0>@  `0 !a`  -<0> @0sww-w '`M`c%0 -S   -<0>0 !  e|  -<0> \0VAGAG}   `` "nQ\aA m[2]# B0sww-w "``nd`g - JvnQ\aAU[3]mn inQ\aAd[1]m njnQ\aAV[3]m/n kjnQ\aAa[1]mA3n i   -<0>0 !n /mn  -<0> N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n .nd  -<0># D0sww-w((`` -n lnQ\aAG[1]mn p -n qnQ\aAW[3]m -n qnQ\aAX[3]mQ Cnsr - ltnQ\aAY[3]mQ Cnuii-./ wnQ\aAb[1]m -n xnQ\aAZ[3]mn 0ynQ\aAc[1]mnz-o?  i - |nQ\aAH[1]m)1n}   -<0>@  }0 !~`  -<0>e,ef @0sww-w '`j}%0 -p   -<0>0 !  |  -<0>? \0VAGAG}   `` "nQ\aA m[2] B0sww-w "``n} - DvnQ\aAA[4]mn nQ\aAh[1]m nnQ\aAB[4]m/n nQ\aAe[1]mA3n    -<0>0 !n /n  -<0># N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n .d  -<0> D0sww-w((`` -n nQ\aAI[1]mn  -n nQ\aAC[4]m -n nQ\aAD[4]mQ Cn - nQ\aAE[4]mQ Cn-./ nQ\aAf[1]m -n nQ\aAF[4]mn 0nQ\aAg[1]mn-?   - nQ\aAJ[1]m)1n   -<0>@  0 !`  -<0> @0sww-w '`%0 -   -<0>0 !  |  -<0> \0VAGAG}   `` "nQ\aA m[2]# B0sww-w "``n - WvnQ\aAG[4]mn nQ\aAl[2]m nnQ\aAH[4]m/n nQ\aAi[1]mA3n    -<0>0 !n /n  -<0> N0 VAGAG} `` "nQ\aA m[1]=m[1]0 !n .d  -<0># D0sww-w((`` -n nQ\aAK[1]mn  -n nQ\aAI[4]m -n nQ\aAJ[4]mQ Cn - nQ\aAK[4]mQ Cn-./ nQ\aAj[2]m -n nQ\aAL[4]mn 0nQ\aAk[2]mn-?   - nQ\aAL[1]m)1n   -<0>@  0 !`  -<0>e,ef @0sww-w '`%0 -   -<0>0 !  |  -<0>? \0VAGAG}   `` "nQ\aA m[2] B0sww-w "``n /#Given the boundary line, AB, transports the hyperbolic segment ML to another hyperbolic segment with an end point C and direction CD.