GSP4„m‡è†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.$è¡LHome` a b c d e f g h i j k l m n o p q _ ,#GSP4_W_0502/Apr 18 20020#` ±Arial o³³ '''$'ÿë$'€ë$'€ë$'ÿÿë$'€€ë$'€ë$'ÿÿë$'ÿÿÿë$'ÀÀÀë$' ë$' ë$' ë%'&'8'8'8'9':'Ð (üü&(ؘ(­×Ð 4üü2%(<0><0><0><0>>ؘ%(2Ñ×Ðÿ ™€h@ðr@×é‡ö†{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ê L3/Triangle (By Edge) ±Arial o³ ³ ÐEÕ˜nÁQ\aAAØ™ôr¡ ` é èv¡ ` é ×Ð Õ˜nÁQ\aABØ™˜—¡ ` é p–¡ ` é ×Ð Ò×Ð Ò×Ð Ò×Ð -ÿÿÿ ÒÕ˜nÁQ\aAAØ×Ð4ÿ``nÒ×Ð Ò×Ð Ò× ´‚/#Constructs and equilateral triangle from two points that determine one edge. The two points will be selected in clockwise order.ë‡ö†{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.$êL3/Triangle (Inscribed) ±Arial o³ ³ Ðc Õ˜nÁQ\aACenterØ™Ü}¡ ` é È}¡ ` é ×Ð Õ˜nÁQ\aARadiusØ™„•¡ ` é Г¡ ` é ×Ð Ò×Ð Ò×Ð -ÿÿÿ ÒÕ˜nÁQ\aACØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aADØ×Ðn Ò×Ðn Ò×Ð-ÿÿÿn ÒÕ˜nÁQ\aABØ×Ð-ÿÿÿn ÒÕ˜nÁQ\aAAØ×Ð4ÿ``nÒ  ×Ð Ò ×Ð Ò ×Ð Ò × ´\/#Constructs an equilateral triangle inscribed in a circle with the given center and radius.ë‡ö†{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$êL4/Square (By Diagonal) ±Arial o³ ³ ÐaÕ˜nÁQ\aAAØ™×ÐÕ˜nÁQ\aABØ™×Ð Ò×Ð ÿÿÿÒÕ˜nÁQ\aADØ×Ðn Ò×Ð@ n Ò×Ð -ÿÿÿn ÒÕ˜nÁQ\aABØ×Ð/n ÒÕ˜nÁQ\aAjØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aACØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aAAØ×Ð5ÿ`ÿnÒ  ×Ð Ò ×Ð Ò ×Ð Ò ×Ð Ò × ´./#Constructs a square from 2 pts on a diagonal.ë‡ö†{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.$êL4/Square (By Edge) ±Arial o³ ³ ÐgÕ˜nÁQ\aAAØ™×ÐÕ˜nÁQ\aABØ™×Ð Ò×Ð Ò×Ð@  Ò×Ð/ ÒÕ˜nÁQ\aAlØ×Ð/n ÒÕ˜nÁQ\aAjØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aABØ×Ðn Ò×Ð.n ÒÕ˜nÁQ\aAkØ×Ð -ÿÿÿn Ò Õ˜nÁQ\aAAØ×Ð5ÿ`ÿnÒ ×Ð Ò ×Ð Ò × ´</#Construct a square from two points that determine an edge.të‡ö†{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$ê L4/Square (Inscribed) ±Arial o³ ³ Ði Õ˜nÁQ\aARadiusØ™×Ð Õ˜nÁQ\aACenterØ™×Ð Ò×Ð@  Ò×Ð -ÿÿÿ ÒÕ˜nÁQ\aABØ×Ð/n ÒÕ˜nÁQ\aAjØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aACØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aAAØ×Ð5ÿ`ÿnÒ×Ð Ò×Ð Ò×Ð Ò×Ð Ò× ´N/#Construct a square inside the circle determine by the given center and radiusë‡ö†{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.$êL5/Pentagon (By Edge) ±Arial o³ ³ ÐEÕ˜nÁQ\aAAØ™ ×ÐÕ˜nÁQ\aABØ™ ×Ð@  Ò×Ð Ò×Ð Ò×Ð@  Ò×Ð Ò×Ð/ ÒÕ˜nÁQ\aAjØ×Ð ÿÿÿnÒÕ˜nÁQ\aAAØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aABØ×Ðn Ò ×Ð -ÿÿÿn Ò Õ˜nÁQ\aACØ×Ðn Ò ×Ðn Ò ×Ðn ÒÕ˜nÁQ\aAc[1]Ø×Ð -ÿÿÿn Ò Õ˜nÁQ\aAFØ×Ð -ÿÿÿn Ò Õ˜nÁQ\aAEØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aADØ×Ðn Ò×Ð6`ÿ`nÒ×Ð Ò×Ð Ò×Ð Ò× ´Ž/#Constructs a regular pentagon with an edge determjined (in clockwise order) by the two given points. By connecting the non-adjacent vertices, instead of adjacent vertices, you can construct a regular pentagram (also known as a pentacle, pentalpha, or pentangle). This self-intersecting regular polygon was the symbol of the Order of the Pythagoras, a 6th century B.X. secret society of geometers.ë‡ö†{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$êL5/Pentagon (Inscribed) ±Arial o³ ³ Ðc Õ˜nÁQ\aACenterØ™×Ð Õ˜nÁQ\aARadiusØ™×Ð Ò×Ð Ò×Ð/ ÒÕ˜nÁQ\aAjØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aAGØ×Ðn Ò×Ð ÿÿÿnÒÕ˜nÁQ\aAFØ×Ðn Ò×Ð -ÿÿÿn Ò Õ˜nÁQ\aAEØ×Ðn Ò ×Ð -ÿÿÿn Ò Õ˜nÁQ\aACØ×Ð-ÿÿÿn Ò Õ˜nÁQ\aADØ×Ðn Ò ×Ðn Ò ×Ðn Ò ×Ð-ÿÿÿn ÒÕ˜nÁQ\aAAØ×Ðn Ò ×Ðn Ò ×Ð-ÿÿÿn ÒÕ˜nÁQ\aABØ×Ð6`ÿ`nÒ  ×Ð Ò ×Ð Ò× ´N/#Constructs a regular pentagon from a circle with the given Center and Radius.ë‡ö†{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.$êL6/Hexagon (By Edge) ±Arial o³ ³ ÐdÕ˜nÁQ\aAAØ™ÿÿÿÿ×ÐÕ˜nÁQ\aABØ™ÿÿÿÿ×Ð Ò×Ð Ò×Ð Ò×Ð-ÿÿÿ ÒÕ˜nÁQ\aAAØ×Ðn Ò×Ð-ÿÿÿn ÒÕ˜nÁQ\aADØ×Ð-ÿÿÿn ÒÕ˜nÁQ\aAEØ×Ðn Ò×Ðn Ò ×Ðn Ò ×Ð -ÿÿÿn Ò Õ˜nÁQ\aABØ×Ðn Ò ×Ðn Ò ×Ð-ÿÿÿn ÒÕ˜nÁQ\aACØ×Ð7`ÿÿnÒ ×Ð Ò×Ð Ò × ´b/#Construct a regular hexagon from two points that determine (in clockwise order) one of the edges.ë‡ö†{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$êL6/Hexagon (Inscribed) ±Arial o³ ³ Ðr Õ˜nÁQ\aACenterØ™ >é à×Ð Õ˜nÁQ\aARadiusØ™ >é ×Ð Ò×Ð@  Ò×Ð Ò×Ð -ÿÿÿ ÒÕ˜nÁQ\aACØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aAEØ×Ðn Ò×Ðn Ò×Ðn Ò×Ðn Ò×Ðn Ò×Ð -ÿÿÿn Ò Õ˜nÁQ\aADØ×Ð -ÿÿÿn Ò Õ˜nÁQ\aAAØ×Ðn Ò ×Ðn Ò×Ðn Ò×Ðn Ò ×Ðn Ò×Ð -ÿÿÿn ÒÕ˜nÁQ\aABØ×Ð7`ÿÿnÒ ×Ð Ò×Ð Ò× ´P/#Given the center and radius of a circle construct an inscribed regular hexagon.ë‡ö†{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.$êL8/Octagon (Inscribed) ±Arial o³ ³ Ðr Õ˜nÁQ\aACenterØ™ >é À×Ð Õ˜nÁQ\aARadiusØ™ >é ð×Ð Ò×Ð Ò×Ð/ ÒÕ˜nÁQ\aAlØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aAEØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aABØ×Ð/n ÒÕ˜nÁQ\aAmØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aADØ×Ðn Ò×Ðn Ò ×Ð ÿÿÿnÒ Õ˜nÁQ\aAIØ×Ð ÿÿÿnÒ Õ˜nÁQ\aAHØ×Ð/n Ò Õ˜nÁQ\aAkØ×Ð/n Ò Õ˜nÁQ\aAjØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aAFØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aAGØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aACØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aAAØ×Ðn Ò×Ðn Ò×Ðn Ò ×Ðn Ò×Ð``ÿn$Ò Õ˜nÁQ\aAP[1]Ø×Ðn Ò×Ðn Ò ×Ðn Ò×Ðn Ò× ´V/#Given a center a radius of a circle, construct an regular octagon inscribed therein.ë‡ö†{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.$êUL17-gon (Inscribed) ±Arial o³³ Ðe Õ˜nÁQ\aARadiusØ™àN¶×Ð Õ˜nÁQ\aACenterØ™ x 8G T Q ×Ð Ò×Ð?  Ò×Ð/ ÒÕ˜nÁQ\aAkØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aASØ×Ðn Ò×Ð ÿÿÿnÒÕ˜nÁQ\aATØ×Ðn Ò×Ð ÿÿÿnÒ Õ˜nÁQ\aACØ×Ðn Ò ×Ð@ n Ò ×Ð -ÿÿÿn Ò Õ˜nÁQ\aADØ×Ðn Ò ×Ð -ÿÿÿn Ò Õ˜nÁQ\aAUØ×Ðn Ò ×Ð ÿÿÿnÒÕ˜nÁQ\aAVØ×Ð@ n Ò ×Ð -ÿÿÿn Ò Õ˜nÁQ\aAWØ×Ð@ n Ò ×Ð -ÿÿÿn ÒÕ˜nÁQ\aAXØ×Ðn Ò ×Ð ÿÿÿnÒÕ˜nÁQ\aAYØ×Ð@ n Ò ×Ð -ÿÿÿn ÒÕ˜nÁQ\aAEØ×Ð/n Ò Õ˜nÁQ\aAlØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aAZØ×Ð,nÒ Õ˜nÁQ\aAmØ×Ð -ÿÿÿn ÒÕ˜nÁQ\aAA[1]rØ×Ðn Ò×Ð ÿÿÿnÒÕ˜nÁQ\aAB[1]rØ×Ðn Ò×Ð -ÿÿÿn Ò Õ˜nÁQ\aAC[1]rØ×Ðn Ò!×Ð -ÿÿÿn Ò"Õ˜nÁQ\aAD[1]rØ×Ð -ÿÿÿn Ò"Õ˜nÁQ\aAE[1]rØ×Ð/n Ò#Õ˜nÁQ\aAnØ×Ð/n Ò$Õ˜nÁQ\aAoØ×Ð -ÿÿÿn Ò&Õ˜nÁQ\aARØ×Ð -ÿÿÿn Ò%Õ˜nÁQ\aAKØ×Ð -ÿÿÿn Ò%Õ˜nÁQ\aAGØ×Ð -ÿÿÿn Ò&Õ˜nÁQ\aAF[1]rØ×Ð,nÒ)*Õ˜nÁQ\aApØ×Ð,nÒ('Õ˜nÁQ\aAqØ×Ðn Ò('×Ð -ÿÿÿn Ò+Õ˜nÁQ\aAG[1]rØ×Ð -ÿÿÿn Ò,Õ˜nÁQ\aAH[1]rØ×Ðn Ò(-Õ˜nÁQ\aAc[3]rØ×Ðn Ò)-Õ˜nÁQ\aAc[4]rØ×Ðn Ò-Õ˜nÁQ\aAc[5]rØ×Ð -ÿÿÿn Ò0Õ˜nÁQ\aAJØ×Ð-ÿÿÿn Ò1Õ˜nÁQ\aAHØ×Ðn Ò/-Õ˜nÁQ\aAc[6]rØ×Ð-ÿÿÿn Ò2Õ˜nÁQ\aAQØ×Ðn Ò'/×Ðn Ò/(×Ðn Ò).×Ðn Ò.*×Ðn Ò3-Õ˜nÁQ\aAc[7]rØ×Ðn Ò4-Õ˜nÁQ\aAc[8]rØ×Ð-ÿÿÿn Ò5Õ˜nÁQ\aAOØ×Ð,nÒ6Õ˜nÁQ\aArØ×Ðn Ò*6×Ð -ÿÿÿn Ò;Õ˜nÁQ\aAMØ×Ð -ÿÿÿn Ò<Õ˜nÁQ\aALØ×Ð,nÒ=Õ˜nÁQ\aAjØ×Ð -ÿÿÿn Ò>Õ˜nÁQ\aAPØ×Ðn Ò='×Ðn Ò@-Õ˜nÁQ\aAc[2]rØ×Ðn ÒA-Õ˜nÁQ\aAc[1]rØ×Ð -ÿÿÿn ÒBÕ˜nÁQ\aANØ×Ðn Ò3A×Ðn ÒA@×Ðn Ò@4×Ðn Ò6C×Ðn ÒC×Ð -ÿÿÿn ÒEÕ˜nÁQ\aAFØ×Ð-ÿÿÿn ÒFÕ˜nÁQ\aAIØ×Ðn ÒG×Ðn ÒG=×Ѐ€€nHÒ(N3A@4M).*6CG='/Õ˜nÁQ\aAP[1]Ø×Ðn Ò(N×Ðn ÒN3×Ðn Ò4M×Ðn ÒM)× ´ø/#Construct a regular 17-gon inscribed in a circle with the given center and radius. This construction realizes Karl Friedrich Guass' discovery of the constructability of the regular 17-gon; the actual construction is due to Richmond through Dixon.ë‡ö†{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.$ê Lsemicircle ±Arial o³³ ÐÕ˜nÁQ\aABØ™ÿÿÿÿ E˜ ×Ð Õ˜nÁQ\aAAØ™ÿÿÿÿðE˜ ×Ѐ Ò×Ð ÿ ÒÕ˜nÁQ\aADØ×Ѐn Ò×Ð ÿnÒÕ˜nÁQ\aACØ×ÐQ C€nÒ×ÐR DÿÿÒ× ´ë‡ö†{A tool in this document was created with a newer version of Sketchpad and cannot be read. The document will open as a copy.aA tool in this document was created with a newer version of Sketchpad and may not work correctly.$êLrectanglelengthtwicewidth ±Arial o³³ ÐtÕ˜nÁQ\aABØ™moc-cam¥orptcap×ÐpÕ˜nÁQ\aAAØ™repleH deH elif¥×Ѐ¥ Ò×Ð/€¥ ÒÕ˜nÁQ\aAlØ×Ð/€n ÒÕ˜nÁQ\aAkØ×Ð ÿnÒÕ˜nÁQ\aAEØ×Ѐn Ò×Ð -ÿn ÒÕ˜nÁQ\aACØ×Ð/€n ÒÕ˜nÁQ\aAjØ×Ð -ÿn Ò Õ˜nÁQ\aADØ×Ѐn Ò×Ѐn Ò ×Ѐn Ò ×Ð5ÿÿnÒ × ´ë‡ö†{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.$êLisoc_right_triangle ±Arial o³ ÐnÕ˜nÁQ\aAAØ™ k@€h@×Ð@Õ˜nÁQ\aAJØ™×Ѐ ÒÕ˜nÁQ\aAjØ×Ð?€n Ò$Óð¿Ðrï¼€V@×Ðÿ Ò$Óð¿Ðrï¼€V@×Ѐ Ò× ´ë‡…