ZXTape! 0Created with Ramsoft MakeTZX2o#'O' Level Maths Revision - Geometry Rose Software1984English EducationalFullNoneOriginal Releaseg1 qqUs 32743 b23613=\+256*23614>\,0:23613=\+1+256*23614>\,0 7:7:7::9 ;0,0;" Program loading ";0,18;1;" PLEASE WAIT ";0:0,0;:"sc":1:1:1:0,0;:"gr""s",24:0,0;:"1": sc @           88     8?88;?88 8            @     ||@~<<~B<>?   88     8?88;?88 8   ?  B    H  B8<8h88x<B@@B@@BB           88     888;888     !       B    H  B DD TD<0DDB@|B<|BB           8?;;8   ??>;?8?  &0    2   0"   ! (  | DD ??;;8   ;8     0      ?@ 8              8  8      8|8888888                    ""  88           ?88   8|88;888        ?      $B   0  ! $B   $   $   D [     UJk5R      $T*Q$Y|     ddD!DIE""&&    / &$D"$Ad0    @D"!D"! Aa    # $@  ? >    mv      ꔫ5)Wh    ?$I)($   BI"IDB!8    |0!H  >  ?`DB!B" s    / $P    ? 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";k:"0","40":"56","0":"0","31":"56","0" nPv=v+1:.5,-10 :1.5@,-20:"20","0";a$::"120" t9۰"1":"18","8";" * WELL DONE * ":۰"0":u=u+"1" wZ.2~L,2:.2~L,2:.2~L,4:.2~L,4:.5,9 xk"20","0";a$:a$="":"9000":"3","7";" TOTAL CORRECT: ";u;"6","7";" TOTAL INCORRECT: ";v yB568,152:151+8*(u>9 )+8*(u>99c),0:568,143:151+8*(u>9 )+8*(u>99c),0:568,128:151+8*(v>9 )+8*(v>99c),0:568,119w:151+8*(v>9 )+8*(v>99c),0: z."16","6";"MORE EXAMPLES? y OR n":0  q$=:q$"y"q$"n"122z q$="y": L"200":"0","14";" END ";"21","9";"Press any key":0:"6" ٰ"2":ڰ"7":"7": N98b,126~:60<,-60<:98b,66B:60<,60< ^30,-30,-:-30,-30,-:-30,-30,-:-30,30,- ѡ-30,30,-:30,30,-:30,30,-:30,-30,-:9 :9 ,14;"ROSE";10 ,12 ;"SOFTWARE": ,ڰ"6":"6"::"990":"995" /np$(2)="alternate angles":p$(1)="vertically opposite angles":p$(3)="corresponding angles" 2N"229","164":13 ,-12 ,-/2:"2","29";"a":l="1":"80" 8o"9000":"990":"995":"216","116":12 ,-12 ,-3*/7:"8","27";"a":l="2":"80" >r"9000":"990":"995":"196","102":12 ,-11 ,/2:ް"1":"9","25";"a":ް"0":l="3":"80" DP"9000":"990":"214","116":-18,-12 ,/2:"8","25";"b" Gll="2":p$(1)="complementary (a+b)=90":p$(2)="supplementary (a+b)=180":p$(3)="equal" Jj"2","0";"Which of the";"4","0";"following";"6","0";"is true?";"9","0";"a and b are:-":"80" h{"9000":"910":p$(1)="c=a+b":p$(2)="b=c+a":p$(3)="a=b+c":a$=" EXT. = sum of INT. opp. s " k"0","0";" REVISION ";"1","0";" QUESTIONS ";"3","0";"What can we say";"5","0";"about angles";"7","0";"a,b and c?" nHް"1":"2","19";"a":ް"0":"150","152":17,2,/2 q>"8","16";"b":"128","118":9 ,-15,-/2 tW"8","27";"c":"206","113":21,-10 ,-/2:l="1":"80":"9000" Vc=((*6)+2)*10 :a=((*6)+2)*10 :c=a400 "700":"800" _"a'?":a$=" CORRESPONDING ANGLE with "+a+"":l="1":"80":"122"+"8878"*(ind="0") d"700":"800":"b'?":a$="a and b are CORRESPONDING ANGLES":"80":"122"+"8878"*(ind="0") Q"700":"800":"c'?":a$="  ALTERNATE ANGLE with "+c+"":l="2":"80" "122"+"8878"*(ind="0") ng=(*8)+2:e=((*6)+2)*10 :f=((*6)+2)*10 :e=f466 ޡ"750":"800":"a'?":p$(1)=(e-g)+"":p$(2)=(f-g+e)+"":p$(3)=(180-e-f)+"":a$="since a+"+g+"="+e+" ALTERNATE ANGLES" *l="1":"80":"122"+"8878"*(ind="0") "750":"800":"b'?";"8","17";e-g;"":a$=" THE 3 s OF A TRIANGLE = 180 ":l="3":"80":"122"+"8878"*(ind="0") "750":"800":"c'?";"8","17";e-g;"":a$="since c and "+(e-g)+" are ALTERNATE s":l="1":"80":"122"+"8878"*(ind="0") "750":"800":"d'?";"8","17";e-g;"":a$="since d="+(e-g)+"+"+f+" EXTERIOR OF ":l="2":"80":"122"+"8878"*(ind="0") 0na=((*6)+2)*10 :e=((*7)+11 )*10 :e=180-ae=90Z+a5600 9F"850":"800":"a'?":a$="since a and "+a+" are ALTERNATE s" \,0:23613=\+1+256*23614>\,0 7:7:7::9 ;0,0;" Program loading ";0,18;1;" PLEASE WAIT ";0:0,0;:"sc":1:1:1:0,0;:"gr""q",40(:0,0;:"2": sc @&           88     8?88;?88 8            @     ||@~<<~B<>?   88     8?88;?88 8   ?  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y OR n":0 q$=:q$"y"q$"n""125" q$="y"ڰ"5":"5":: "200":"0","14";" END ";"21","9";"Press any key":"112","175":"40","0":"0","-8":"-40","0":"0","8":"0":"6" Ȩٰ"2":ڰ"7":"7"::"98","126":"60","-60":"98","66":"60","60":30,-30,-:-30,-30,-:-30,-30,-:-30,30,- ђ-30,30,-:30,30,-:30,30,-:30,-30,-:ٰ"9":"9","14";"ROSE";"10","12";"SOFTWARE": ,~n="0":m="16":l="0":"990":p$="t":ް"1":"3","19";"a";"3","29";"a";"9","20";"b";"9","30";"b":ް"0":"920" 23a$="CONGRUENT 2s and 1 side (AAS)":"100" 8M"990":p$="f":ް"1":"3","19";"a";"3","29";"a":ް"0":"920":"930" ;Wp$="f":a$="THIS IS NOT PROOF OF CONGRUENCY (must be the included angle)":"100" >["990":p$="t":"920":"930":"940":a$=" CONGRUENT 3 sides equal (SSS)":"100" A}"990":"920":"940":ް"1":"3","19";"a";"3","29";"a":ް"0":a$="CONGRUENT 2 sides & included (SAS)":"100" Jm="16":l="0":n="0":"980":n="64":l="16":"910":ް"1":"2","0";"These two";"4","0";"triangles";"6","0";"are similar";5,22;"a";3,29;"a";9 ,22;"b";9 ,30;"b" P"9","18";"c";"9","25";"c":ް"0":"11","31";"P";"11","23";"Q";"11","17";"R":i=(*4)+1:j=(*2) S"6","17";i;"cm";"3","25";2*i;"cm";"12","17";"<-";2*i;"cm->";"9","0";"SO the length";"11","0";"of PR is ";4*i+2*j*i;"cm":p$="t":j="0"p$="f" Y`a$="since "+i+"/"+(2*i)+"=QR/PQ giving PR="+(2*i)+"+"+(4*i)+"cm":"100" h"950":"2","0";"Triangles ABC";"4","0";"and APQ are";"6","0";"similar";"8","0";"SO the length";"10","0";"of PQ is "; kvi=((*3)+2)*2:"970":i/2+j;"cm";"11","23";i;"cm";"11","19";"<--";"11","27";"-->" nMa$=" Remember P and Q are midpoints   of AB and AC ":"100" w%"950":i=(*9 )+"1":"970" z"2","0";"If the area of";"4","0";" APQ is ";i;" sq.cm";"6","0";"THEN the area of";"8","0";" ABC is ";i*(4-2*j);" sq.cm" }Qa$=" DOUBLING THE DIMENSIONS GIVES   FOUR TIMES THE AREA ":"100" m="-16":"910":"180","175":"16","-80":"176","160":"4","-4":"180","160":"-4","-4":"186","160":"4","-4":"190","160":"-4","-4" ii=(*7)+"2":"970":"4","17";i;" cm";"4","27";i+1;" cm";"11","19";"<-b-> <-a->" "0","0";" The ";"2","0";"topmost angle";"4","0";"is bisected.";"6","0";"SO";"8","0";"a = ";i+1-j;"9","0";"b ";i+j `"0","103":"6","0":"32","103":"6","0":j="1"a$="since a/b = "+(i+1)+"/"+i "100" n="0":m="-32":l="0":"910":"0","23";"A";"11","23";"C";"11","31";"B":"188","100":"4","0":"0","-4":i=((*2)+1)*2+"1":"970" "5","19";i+1+6*(i=5);"cm";"11","26";i;"cm";"0","0";" PYTHAGORAS THEOREM ";"2","0";"states c=a+b";"4","0";"in a rt d ";"7","0";"SO";"9","0";"AB=";i+2+6*(i=5)+j;" cm" 3a$=" 3,4,5 and 5,12,13 are rt d s ":"100" ̚"900":"0","28";"m";"0","0";" SYMMETRY ";"2","0";"m is a mirror line";"4","0";"or line of symmetry";"6","0";"for this equilateral " 3a$=" Equilateral has 3 such lines ":"970" W"9","0";"SO it has ";3+3*j;"11","0";"lines of symmetry":"100" "0","0";" ROTATIONAL SYMMETRY ";"2","0";"By rotating equilateral","ABC through 120","about P, we get the","same picture" m"970":"8","0";"By making ";3+j;" such","rotations, A",,"returns to its",,"original position" "900":"255","96":"-60","35":"180","93":"65","38":ް"1":"1","26";"A";"11","31";"B";"11","23";"C";"8","28";"P":ް"0" Da$=" Order of rotational symmetry=3 ":qu="1":"100":"330" l"255","96":"-70","0":"35",35#*3:"35",-35#*3:"220","175":"0","-96": j252-n,"95":-64@+l,"0":32 +m-l/2,64@-l:32 -m-l/2,-64@+l: 8"128","128":"6","-3":"208","128":"6","-3": f"144","90":"0","8":"146","90":"0","8":"224","90":"0","8":"226","90":"0","8": "160","128":"6","3":"161","126":"6","3":"162","124":"6","3":"240","128":"6","3":"241","126":"6","3":"242","124":"6","3": ?n="16":l="-16":m="16":"980":"184","132":"40","0" "228","112":"6","3":"228","114":"6","3":"216","152":"6","3":"216","154":"6","3":"170","120":"6","-3":"197","160":"6","-3" O"204","135":"3","-3":"-3","-3":"204","98":"3","-3":"-3","-3" S"0","27";"A";"5","29";"P";"9","30";"B";"9","18";"C";"5","21";"Q": (j=(*2):p$="t":j="1"p$="f"  3ڰ"5":"5"::" SIMILAR TRIANGLES ":"910": ޜڰ"5":"5"::" CONGRUENCY OF TRIANGLES ":"910":n="80":"910":n="0":"4","0";"These two";"6","0";"triangles";"8","0";"are congruent": #("""9000" #+5"21","9";"Press any key":0:="""9003" #."""9006" #1װ".05","4":: uvnmlijQnO PtA$CONGRUENT 2s and 1 side (AAS) g3 qqWs 32743 b23613=\+256*23614>\,0:23613=\+1+256*23614>\,0 7:7:7::9 ;0,0;" Program loading ";0,18;1;" PLEASE WAIT ";0:0,0;:"sc":1:1:1:0,0;:"gr""s",24:0,0;:"3": sc @           88     8?88;?88 8            @     ||@~<<~B<>? 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";k:"0","48":"55","0":"0","39":"55","0" nAv=v+"1":װ".5","-10":װ"1.5","-20":"19","0";a$::"120" t9۰"1":"17","8";" * WELL DONE * ":۰"0":u=u+"1" w<װ".2","2":װ".2","2":װ".2","4":װ".2","4":װ".5","9" xU"19","0";a$:a$="":"9000":"4":ڰ"4"::"3","7";" TOTAL CORRECT:  ";u y"6","7";" TOTAL INCORRECT: ";v:"56","152":"135","0":"56","143":"135","0":"56","128":"135","0":"56","119":"135","0":qu="1""125" z"9000":ڰ"6":"6":: }."16","6";"MORE EXAMPLES? y OR n":0 q$=:q$"y"q$"n""125" q$="y""6":ڰ"6":: "200":"0","14";" END ";"21","9";"Press any key":"113","175":"38","0":"0","-7":"-38","0":"0","7":"0":"6" ٰ"2":ڰ"7":"7": 6"98","126":"60","-60":"98","66":"60","60" ^30,-30,-:-30,-30,-:-30,-30,-:-30,30,- ѡ-30,30,-:30,30,-:30,30,-:30,-30,-:9 :9 ,14;"ROSE";10 ,12 ;"SOFTWARE": ,;:r="0":n="88":l="0":m="0":"900":"910":"920" /Z"2","0";"How many lines";"4","0";"of symmetry does";"6","0";"a rectangle have?" Ga="2":p$(1)="four":p$(2)="two":p$(3)="eight":a$=" The diagonals are NOT mirror-   lines or lines of symmetry ":80P Jn="72":l="-16":m="16":"900":"910":"2","0";"What is the order";"4","0";"of rotational";"6","0";"symmetry for a";"8","0";"parallelogram?" MW"4","25";"P":p$(3)="zero":a$=" BY ROTATING 180 ABOUT P TWICE ":"80" hIl="-40":m="40":"900":"910":"187","134":"3","5":"5","-3" kh"172","158":"0","5":"212","102":"0","5":"153","131":"5","2":"223","134":"5","2" ne"2","0";"What is the";"4","0";"name of";"6","0";"this special";"8","0";"parallelogram?" qp$(1)="rhombus":p$(2)="trapezium":p$(3)="rectangle":a=1:a$=" 4 SIDES EQUAL & DIAGS.AT RT.s ":80P pn="104":l="40":m="24":"900":"202","101":"3","3":"-3","3":"202","157":"3","3":"-3","3" "2","0";"What is the";"4","0";"name of this";"6","0";"quadrilateral?":p$(3)="parallelogram":a="2":a$=" 2 OPPOSITE SIDES ARE PARALLEL ":"80" mr="4":"900":"0","23";"<-a->";"9","18";"<---- b ---->";"4","26";"h":"204","164":"0","-56" f"2","0";"What is the";"4","0";"formula for";"6","0";"the area of";"8","0";"a trapezium?" Sp$(1)="(aXb)/h":p$(2)="hX(a+b)/2":p$(3)="(aXh)-b/2":80P b"960":"229","100":"195","100":"178","130":"195","162":"230","169":"247","132" "2","0";"The sum of the";"4","0";"interior angles";"6","0";"of an n-sided";"8","0";"polygon is";"10","0";"(2n-4)X90" "14","0";" FOR  this irregular hexagon";"16","0";"the sum is (2X6-4)X90";"18","0";"=(12-4)X90 = 8X90 = 720":"9000" n="80":"900":"2","0";"What is the";"4","0";"sum of the";"6","0";"interior angles";"8","0";"of a quadrilateral?" qi=(*2)+"1":p$(1)=(i*90Z)+"":p$(2)="360":p$(3)=((i+1)*90Z)+"" 2a$="PUT n=4 INTO (2n-4)X90 ANS.360":"80" 0X"960":"192","96":"-16","0":"186","99":"10","23";"^";"11","23";"ext " 3["15","0";"The SUM of the exterior angles";"17","0";"of ANY polygon = 360":"9000" Ny"970":"5","30";"?";"2","0";"How many degrees";"4","0";"in one interior ";"6","0";"of a regular hexagon?" QNa="2":p$(2)="120":a$=" DIVIDE THE SUM (2n-4)X90 BY 6 ":"80" Xm"970":"191","166":20,-20*3:"39","0":ް"1":"4","26";"?";"6","26";"O":ް"0" [p"2","0";"O is the centre.";"4","0";"What is the";"6","0";"value of the";"8","0";"angle marked '?'" ^2a$=" SINCE IT IS ONE-THIRD OF 360 ":"80" v"970":"232","166":"-60",-20*3:ް"1":"3","23";"?";"0","23";"A";"0","29";"B";"5","20";"C":ް"0" y"2","0";"What is the";"4","0";"value of ACB ?":p$(2)="30":i=(*6)*5+35#:p$(1)=i+"":p$(3)=(i+5)+"" |1a$=" ABC IS ISOSCELES & BAC=120 ":"80" N"970":"192","96":"-16","0":"186","99":ް"1":"8","22";"y":ް"0" r"2","0";"A regular n-sided";"4","0";"polygon has";"6","0";"exterior S of y";"8","0";"SO n = ?" up$(2)="360/y":p$(1)="360/(180-y)":p$(3)="6y":a$=" SUM OF EXT.s = 360 = n X y ":80P Dz=((*3)+3)*10 :"800":"CAB ?":"233","124" ]p$(2)=(502+z)+"":p$(1)=(90Z-z)+"":p$(3)=(z+40()+"" aa$="CEF=90-40=DEA & DAE=180-50-"+z+"  SO CAB=180-"+(130-z):80P "800":"DBC ?";"4","29";502+z;"5","30";" ";"6","29";"<":"244","134":-6,-11 ,-/1.5@:"242","100":a="1" >a$=" SUM OF ANGLES OF = 180 ":qu="1":"80":"590"  Q"248","96":"-64","0":"51","33":"248","96":"-32","79":"0","-79" #_"216","100":"4","0":"0","-4":"1","22";z;"->";"10","23";"^";"11","23";"40" &"0","28";"D";"6","26";"E";"10","27";"F";"5","30";"A";"10","31";"B";"9","22";"C";"0","0";" EXERCISE ";"2","0";"What is the";"4","0";"value of "; (4"0","175":"79","0":"0","168":"79","0": i" REVISION QUESTIONS ":248,104h+r:-n,0:l,568:n-l-m,0:m,-568: <"248","104":-n+l,"56":248-n,"104":n-m,"56": B248-n/2,"104":"0","56":"248","132":-n,"0": "232","96":"-40","0":"-20",20*3:"20",20*3:"40",0+l:"20",-20*3-l:"-20",-20*3: 6"0","0";" REMEMBER THIS:- ":l="8":"950": 7"0","0";" EXERCISE ":"808":l="0":"950": #("""9000" #+5"21","9";"Press any key":0:="""9003" #.""9006.# #1װ".05","4":: uvrnXlmaiPkz(QnO /four two eight AF The diagonals are NOT mirror-   lines or lines of symmetry