diagram stringlengths 16 45 | style stringclasses 2
values | split stringclasses 1
value | category stringclasses 2
values | points listlengths 2 30 | lines listlengths 0 26 | circles listlengths 0 6 | semantics listlengths 0 18 | structure listlengths 1 3 ⌀ | planes listlengths 0 22 ⌀ |
|---|---|---|---|---|---|---|---|---|---|
PGDP/printed/image/PGDP10K_new_0.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"line F E D C",
"line j lieson B E G",
"line k lieson A D H"
] | [] | [
"m \\angle FEG = m \\angle EDH"
] | null | null |
PGDP/printed/image/PGDP10K_new_1.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D"
] | [
"line A D",
"line B C D",
"line A B",
"line A C"
] | [] | [
"BD \\perp AC on C",
"BA = 8",
"BD = 12",
"m \\angle CBA = 60"
] | null | null |
PGDP/printed/image/PGDP10K_new_2.png | printed | train | plane geometry | [
"A",
"B",
"C"
] | [
"line B C",
"line A B",
"line A C"
] | [] | [
"BC \\perp AB on B",
"AC = x",
"BA = CB = 11\\sqrt{2}",
"m \\angle CAB = 45"
] | null | null |
PGDP/printed/image/PGDP10K_new_3.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E"
] | [
"line C D A",
"line C B",
"line A B",
"line E A",
"line E C",
"line E D B"
] | [] | [
"m \\angle ADB = m \\angle CDE",
"m \\angle ADE = m \\angle CDB"
] | null | null |
PGDP/printed/image/PGDP10K_new_4.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [
"line A B D",
"line C D E",
"line H E F",
"line I H G",
"line B I J"
] | [] | [
"m \\angle IBA = 3x+10",
"m \\angle HIJ = 6x-5",
"m \\angle CDB = 2x-5",
"m \\angle FED = 5x",
"m \\angle EHG = 2x"
] | null | null |
PGDP/printed/image/PGDP10K_new_5.png | printed | train | plane geometry | [
"R",
"P",
"Q",
"S"
] | [
"line R S",
"line Q S",
"line P Q",
"line P R"
] | [] | [] | null | null |
PGDP/printed/image/PGDP10K_new_6.png | printed | train | plane geometry | [
"Q",
"P",
"R",
"M"
] | [
"line Q M",
"line Q P",
"line Q R",
"line P M R"
] | [] | [
"QM \\perp PR on M",
"QP \\perp QR on Q",
"PQ = 13",
"MQ = 12"
] | null | null |
PGDP/printed/image/PGDP10K_new_7.png | printed | train | plane geometry | [
"B",
"C",
"D",
"A"
] | [
"line A B C D"
] | [] | [
"AD = 3\\frac{3}{4}",
"AB = BC = CD"
] | null | null |
PGDP/printed/image/PGDP10K_new_8.png | printed | train | plane geometry | [
"S",
"R",
"T"
] | [
"line S T",
"line S R",
"line T R"
] | [] | [
"SR = x+7",
"TS = x-1",
"RT = SR = 3x-5"
] | null | null |
PGDP/printed/image/PGDP10K_new_9.png | printed | train | plane geometry | [
"D",
"E",
"F"
] | [
"line E D",
"line E F",
"line D F"
] | [] | [
"ED \\perp DF on D",
"DE = 20",
"FD = 39",
"EF = 43.8",
"m \\angle EFD = 27"
] | null | null |
PGDP/printed/image/PGDP10K_new_10.png | printed | train | plane geometry | [
"A",
"B",
"C"
] | [
"line A B",
"line C B",
"line A C"
] | [] | [
"CB \\perp AC on C",
"CA = 18",
"BC = 15",
"m \\angle CAB = x"
] | null | null |
PGDP/printed/image/PGDP10K_new_11.png | printed | train | plane geometry | [
"B",
"C",
"A"
] | [
"line C A",
"line B A",
"line B C"
] | [] | [
"CA \\perp BC on C",
"BC = a",
"CA = b",
"AB = c",
"m \\angle ABC = 60",
"m \\angle BAC = 30"
] | null | null |
PGDP/printed/image/PGDP10K_new_12.png | printed | train | plane geometry | [
"P",
"R",
"Q",
"A"
] | [
"line P Q",
"line Q R",
"line P A R"
] | [
"\\odot A lieson P Q R"
] | [
"m \\angle APQ = 3x+1",
"m \\angle ARQ = 7x-1"
] | null | null |
PGDP/printed/image/PGDP10K_new_13.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E"
] | [
"line D A",
"line B C"
] | [
"\\odot E lieson D C B A"
] | [
"AD = 3x+7",
"BC = 5x-9",
"m \\widehat AD = m \\widehat BC = 142"
] | null | null |
PGDP/printed/image/PGDP10K_new_14.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D"
] | [
"line A D",
"line C D"
] | [
"\\odot B lieson A D C"
] | [
"m \\angle ADC = a",
"m \\widehat CA = 116"
] | null | null |
PGDP/printed/image/PGDP10K_new_15.png | printed | train | plane geometry | [
"C",
"B",
"D",
"E",
"A"
] | [
"line C A E",
"line B A D"
] | [
"\\odot A lieson C B E D"
] | [
"m \\angle EAD = 42"
] | null | null |
PGDP/printed/image/PGDP10K_new_16.png | printed | train | plane geometry | [
"A",
"B",
"C"
] | [
"line A C",
"line B C",
"line B A"
] | [] | [
"m \\angle CBA = 40",
"m \\angle BCA = 25",
"m \\angle CAB = x"
] | null | null |
PGDP/printed/image/PGDP10K_new_17.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L"
] | [
"line I H E A",
"line K J D B",
"line F E D C",
"line G H J L"
] | [] | [
"m \\angle IHJ = m \\angle 1",
"m \\angle DJH = m \\angle 2",
"m \\angle EHJ = m \\angle 4",
"m \\angle HED = m \\angle 6",
"m \\angle AEF = m \\angle 5",
"m \\angle BDE = m \\angle 3"
] | null | null |
PGDP/printed/image/PGDP10K_new_19.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"line A B",
"line B E",
"line E H",
"line G F H",
"line C G",
"line A C",
"line D F"
] | [] | [
"GH \\perp DF on F",
"DF = 6"
] | null | null |
PGDP/printed/image/PGDP10K_new_20.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E"
] | [
"line A B",
"line B E",
"line C D E",
"line C A",
"line A D"
] | [] | [
"BE \\perp CE on E",
"CE \\perp AD on D",
"AB \\perp BE on B",
"CA = 8",
"DE = 9",
"m \\angle DCA = 30"
] | null | null |
PGDP/printed/image/PGDP10K_new_21.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [
"line F A",
"line F E",
"line E D",
"line D C",
"line A C",
"line B A"
] | [
"\\odot B lieson F E D C A"
] | [
"BA = 10"
] | null | null |
PGDP/printed/image/PGDP10K_new_22.png | printed | train | plane geometry | [
"C",
"A",
"B",
"D"
] | [
"line C B",
"line A D B",
"line C A",
"line C D"
] | [] | [
"CB \\perp CA on C",
"AB \\perp CD on D"
] | null | null |
PGDP/printed/image/PGDP10K_new_23.png | printed | train | plane geometry | [
"C",
"A",
"E",
"D",
"B"
] | [
"line A B D",
"line C D",
"line E B C",
"line A E"
] | [] | [
"CD = AE",
"BC = EB",
"AB = BD",
"m \\angle BAE = m \\angle BDC"
] | null | null |
PGDP/printed/image/PGDP10K_new_24.png | printed | train | plane geometry | [
"P",
"Q",
"R",
"V",
"T",
"S",
"U"
] | [
"line Q P",
"line Q R",
"line R V S",
"line P T S",
"line U T",
"line U V"
] | [] | [
"m \\angle PQR = m \\angle 1",
"m \\angle TUV = m \\angle 3",
"m \\angle VST = m \\angle 2"
] | null | null |
PGDP/printed/image/PGDP10K_new_25.png | printed | train | plane geometry | [
"A",
"D",
"B",
"E",
"F",
"G",
"C"
] | [
"line G C D",
"line D E",
"line F E",
"line B C F",
"line A B",
"line A G"
] | [] | [] | null | null |
PGDP/printed/image/PGDP10K_new_26.png | printed | train | plane geometry | [
"D",
"E",
"U",
"F",
"T",
"S",
"A"
] | [
"line D A T",
"line S A F",
"line E A U",
"line E S D",
"line D U F",
"line E T F"
] | [] | [
"UA = 2.9",
"TA = 2x-5",
"DA = 6",
"FA = 4.6",
"EA = y",
"SA = 4z"
] | null | null |
PGDP/printed/image/PGDP10K_new_27.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E"
] | [
"line A E",
"line B C E",
"line A C D",
"line A B",
"line B D",
"line E D"
] | [] | [
"EC = 2y+3",
"BC = 4y-11",
"AC = 3y+5",
"DC = 2x+4"
] | null | null |
PGDP/printed/image/PGDP10K_new_28.png | printed | train | plane geometry | [
"A",
"C",
"E",
"F",
"B",
"D"
] | [
"line C F B",
"line A E B",
"line D A",
"line D F",
"line D C",
"line D E"
] | [] | [
"AB \\perp DE on E",
"CB \\perp DF on F"
] | null | null |
PGDP/printed/image/PGDP10K_new_29.png | printed | train | plane geometry | [
"A",
"B",
"C"
] | [
"line A B",
"line C B",
"line C A"
] | [] | [
"BC = 73",
"AB = x",
"m \\angle ABC = 55",
"m \\angle ACB = 60"
] | null | null |
PGDP/printed/image/PGDP10K_new_30.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E"
] | [
"line A B",
"line B C",
"line D B",
"line E B"
] | [
"\\odot B lieson E D C A"
] | [
"BC \\perp DB on B",
"m \\angle CBA = 110",
"m \\angle ABE = x",
"m \\angle EBD = 30"
] | null | null |
PGDP/printed/image/PGDP10K_new_31.png | printed | train | plane geometry | [
"G",
"D",
"F",
"E",
"A",
"B"
] | [
"line G F E",
"line B D F A",
"line D G",
"line D E"
] | [] | [
"GE \\perp BA on F",
"GD = DE = 6.5",
"GF = 5"
] | null | null |
PGDP/printed/image/PGDP10K_new_32.png | printed | train | plane geometry | [
"A",
"B",
"C"
] | [
"line A C",
"line B C",
"line A B"
] | [] | [
"BA = 13",
"AC = x",
"m \\angle CBA = 141",
"m \\angle CAB = 18"
] | null | null |
PGDP/printed/image/PGDP10K_new_33.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D"
] | [
"line B C",
"line C D",
"line B D",
"line A B",
"line A C"
] | [] | [
"CD \\perp BD on D",
"DB = CD = 12",
"CB = y",
"m \\angle BCD = x"
] | null | null |
PGDP/printed/image/PGDP10K_new_34.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E"
] | [
"line B C D E",
"line A B"
] | [
"\\odot C lieson B D"
] | [
"m \\angle CBA = m \\angle 8"
] | null | null |
PGDP/printed/image/PGDP10K_new_35.png | printed | train | plane geometry | [
"X",
"Y",
"Z"
] | [
"line X Z",
"line Y Z",
"line X Y"
] | [] | [
"YX = 4",
"ZY = 7",
"XZ = 6"
] | null | null |
PGDP/printed/image/PGDP10K_new_36.png | printed | train | plane geometry | [
"A",
"B",
"C"
] | [
"line A B",
"line C B",
"line C A"
] | [] | [
"AB \\perp CA on A",
"CA = \\frac{4}{9}",
"AB = x",
"BC = \\frac{8}{9}"
] | null | null |
PGDP/printed/image/PGDP10K_new_37.png | printed | train | plane geometry | [
"B",
"A",
"C",
"E",
"D"
] | [
"line A B",
"line B C",
"line C D",
"line E D",
"line A E"
] | [] | [] | null | null |
PGDP/printed/image/PGDP10K_new_38.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [
"line A B C",
"line F E C",
"line A D F",
"line D B",
"line B E",
"line D E"
] | [] | [
"ED = x",
"DB = y",
"AC = 3x-6",
"CF = 2x+1",
"AD = DF",
"FE = EC",
"BC = AB"
] | null | null |
PGDP/printed/image/PGDP10K_new_39.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D"
] | [
"line A B C",
"line D C",
"line D B",
"line D A"
] | [] | [
"CB = x",
"AB = 4",
"AD = 10",
"CD = 15",
"m \\angle BDA = m \\angle BDC"
] | null | null |
PGDP/printed/image/PGDP10K_new_42.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [
"line A B",
"line F C B",
"line E F",
"line E D A",
"line D C"
] | [] | [
"EF \\parallel AB",
"FE = 11",
"AB = x",
"DC = 8",
"ED = DA",
"FC = CB"
] | null | null |
PGDP/printed/image/PGDP10K_new_43.png | printed | train | plane geometry | [
"M",
"N",
"R",
"Q",
"P"
] | [
"line M N",
"line Q P N",
"line Q R",
"line M P R"
] | [] | [
"QP = PR",
"MP = PN"
] | null | null |
PGDP/printed/image/PGDP10K_new_45.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D"
] | [
"line A B",
"line B C",
"line D C",
"line A D",
"line A C"
] | [] | [
"m \\angle DAC = m \\angle BAC",
"m \\angle ABC = m \\angle DCA"
] | null | null |
PGDP/printed/image/PGDP10K_new_46.png | printed | train | plane geometry | [
"H",
"J",
"K",
"L"
] | [
"line J K",
"line H L K",
"line H J",
"line J L"
] | [] | [
"HK \\perp JL on L",
"HJ = JK = 9",
"HK = 14"
] | null | null |
PGDP/printed/image/PGDP10K_new_47.png | printed | train | plane geometry | [
"T",
"V",
"W",
"S"
] | [
"line S W",
"line V W",
"line T S",
"line T V"
] | [] | [
"ST = a+15",
"TV = 3b+5",
"SW = b+11",
"WV = 3a+11"
] | null | null |
PGDP/printed/image/PGDP10K_new_48.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"line C B D",
"line E F G",
"line A B F H"
] | [] | [
"CD \\parallel EG",
"m \\angle GFB = 7x",
"m \\angle CBF = 8x-10",
"m \\angle EFB = 6y+20"
] | null | null |
PGDP/printed/image/PGDP10K_new_49.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D"
] | [
"line A D",
"line B D",
"line C B",
"line A C",
"line A B"
] | [] | [
"AC = AD",
"m \\angle CAB = m \\angle DAB"
] | null | null |
PGDP/printed/image/PGDP10K_new_50.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [
"line D C E",
"line A C F",
"line B C"
] | [] | [
"DE \\perp AF on C",
"m \\angle ACB = m \\angle 12",
"m \\angle ECB = m \\angle 11",
"m \\angle DCF = m \\angle 13"
] | null | null |
PGDP/printed/image/PGDP10K_new_51.png | printed | train | plane geometry | [
"R",
"S",
"V",
"U",
"T"
] | [
"line S T U",
"line V U",
"line T V",
"line R T",
"line R S"
] | [] | [
"SU \\perp VU on U",
"SU \\perp RS on S",
"UT = 8x+4",
"ST = 11x-2",
"UV = 15x"
] | null | null |
PGDP/printed/image/PGDP10K_new_52.png | printed | train | plane geometry | [
"B",
"A",
"M",
"K"
] | [
"line A M K",
"line A B",
"line B K",
"line B M"
] | [] | [
"AM = MK",
"m \\angle ABM = 30",
"m \\angle MKB = 60",
"m \\angle MAB = 40"
] | null | null |
PGDP/printed/image/PGDP10K_new_53.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D"
] | [
"line B C",
"line A D C",
"line B A",
"line B D"
] | [] | [
"AC \\perp BD on D",
"AB = BC = AC = s",
"BD = \\frac{\\sqrt{3}}{2}s",
"m \\angle ABD = 30",
"m \\angle DAB = 60"
] | null | null |
PGDP/printed/image/PGDP10K_new_54.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E"
] | [
"line A C",
"line C E",
"line B E",
"line B A",
"line A D E",
"line B D C"
] | [] | [
"AD = 2",
"BD = CD = DE = 8"
] | null | null |
PGDP/printed/image/PGDP10K_new_55.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E"
] | [
"line A C",
"line A B",
"line B D",
"line C D",
"line C E B",
"line A E D"
] | [] | [
"AB \\parallel CD",
"AB = CD"
] | null | null |
PGDP/printed/image/PGDP10K_new_56.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"line A B",
"line B C",
"line D C",
"line E D",
"line F E",
"line G F",
"line G H",
"line H A"
] | [] | [
"GF = FE = GH = ED = HA = DC = AB = BC"
] | null | null |
PGDP/printed/image/PGDP10K_new_58.png | printed | train | plane geometry | [
"A",
"C",
"E",
"D",
"O",
"B"
] | [
"line A C B",
"line E O C D",
"line O B",
"line A O"
] | [
"\\odot O lieson E A D B"
] | [
"AB \\perp ED on C"
] | null | null |
PGDP/printed/image/PGDP10K_new_59.png | printed | train | plane geometry | [
"C",
"A",
"B",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"line J K",
"line E K",
"line C G E",
"line G I",
"line H I",
"line F H",
"line F B",
"line B G",
"line A E",
"line D A",
"line D J"
] | [] | [
"EG = CG = 6",
"GI = n"
] | null | null |
PGDP/printed/image/PGDP10K_new_60.png | printed | train | plane geometry | [
"P",
"S",
"R",
"Q",
"A"
] | [
"line S A Q",
"line P A R",
"line S R",
"line Q R",
"line P S",
"line P Q"
] | [
"\\odot A lieson P Q R S"
] | [] | null | null |
PGDP/printed/image/PGDP10K_new_61.png | printed | train | plane geometry | [
"P",
"A",
"B",
"C"
] | [
"line A B",
"line P B",
"line C P",
"line A C"
] | [
"\\odot P lieson A B C"
] | [
"m \\angle BAC = m \\angle 1",
"m \\angle BPC = m \\angle 2",
"m \\widehat BC = 145"
] | null | null |
PGDP/printed/image/PGDP10K_new_62.png | printed | train | plane geometry | [
"E",
"H",
"F",
"G"
] | [
"line H G",
"line E H",
"line E F",
"line G F"
] | [] | [
"EH = HG",
"EF = GF",
"m \\angle EFG = 50",
"m \\angle GHE = 120"
] | null | null |
PGDP/printed/image/PGDP10K_new_63.png | printed | train | plane geometry | [
"D",
"A",
"B",
"C",
"E"
] | [
"line E D A B",
"line A C",
"line B C"
] | [] | [
"m \\angle ABC = x+19",
"m \\angle ACB = x+13",
"m \\angle DAC = 3x"
] | null | null |
PGDP/printed/image/PGDP10K_new_64.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D"
] | [
"line D B",
"line C A B",
"line C D"
] | [
"\\odot A lieson C B D"
] | [
"DB \\perp CD on D",
"DB = 16",
"CD = 30"
] | null | null |
PGDP/printed/image/PGDP10K_new_65.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D"
] | [
"line A C",
"line C D",
"line B D",
"line A B"
] | [] | [
"CD = DB = 1.7"
] | null | null |
PGDP/printed/image/PGDP10K_new_66.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [
"line A B C",
"line C E F",
"line A D F",
"line B D",
"line B E",
"line D E"
] | [] | [
"CF = 6",
"EF = DF"
] | null | null |
PGDP/printed/image/PGDP10K_new_67.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"line A B C",
"line D C",
"line D B",
"line D A",
"line E F G",
"line H G",
"line H F",
"line H E"
] | [] | [
"EG = 12",
"AC = 16",
"DB = 20",
"FH = x",
"AB = BC",
"EF = FG",
"m \\angle FEH = m \\angle BCD",
"m \\angle DAB = m \\angle FGH"
] | null | null |
PGDP/printed/image/PGDP10K_new_68.png | printed | train | plane geometry | [
"O",
"A",
"B",
"C",
"D",
"E",
"F"
] | [
"line D B A",
"line A C F",
"line D E F"
] | [
"\\odot O lieson B C E"
] | [
"AB = 3.5",
"FE = 2",
"DB = 6.8",
"AF = x"
] | null | null |
PGDP/printed/image/PGDP10K_new_69.png | printed | train | plane geometry | [
"G",
"H",
"F"
] | [
"line G F",
"line H F",
"line H G"
] | [] | [
"GF \\perp HF on F",
"GF = x",
"FH = 32",
"m \\angle FHG = 29"
] | null | null |
PGDP/printed/image/PGDP10K_new_71.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [
"line B C E",
"line A C D"
] | [
"\\odot F lieson B A E D"
] | [
"m \\angle ECD = m \\angle 1",
"m \\widehat EA = 122",
"m \\widehat BD = 32"
] | null | null |
PGDP/printed/image/PGDP10K_new_72.png | printed | train | plane geometry | [
"Y",
"X",
"Z",
"C",
"A",
"B",
"D"
] | [
"line Y B Z",
"line X D Z",
"line Y C X",
"line Y A D",
"line C A Z",
"line X A B"
] | [] | [
"XD = DZ",
"BZ = YB",
"YC = CX"
] | null | null |
PGDP/printed/image/PGDP10K_new_73.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G"
] | [
"line E F G",
"line A B C G",
"line F B",
"line B D",
"line F D C"
] | [] | [
"m \\angle ABF = m \\angle 5",
"m \\angle CBD = m \\angle 9",
"m \\angle FBD = m \\angle 6",
"m \\angle BCD = m \\angle 10",
"m \\angle BDC = m \\angle 4",
"m \\angle BDF = m \\angle 3",
"m \\angle GCD = m \\angle 11",
"m \\angle BFD = m \\angle 2",
"m \\angle EFB = m \\angle 1",
"m \\angle GFD = ... | null | null |
PGDP/printed/image/PGDP10K_new_74.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E"
] | [
"line D C",
"line E C",
"line B C",
"line A B",
"line A E"
] | [] | [
"DC = 7"
] | null | null |
PGDP/printed/image/PGDP10K_new_75.png | printed | train | plane geometry | [
"J",
"K",
"M",
"N",
"L",
"Q"
] | [
"line K L",
"line J K",
"line J L",
"line M Q",
"line M N",
"line Q N"
] | [] | [
"KL = MQ",
"MN = JL",
"m \\angle LKJ = m \\angle MQN"
] | null | null |
PGDP/printed/image/PGDP10K_new_76.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"line q lieson A C G",
"line p lieson H D F",
"line E D C B"
] | [] | [
"m \\angle FDE = m \\angle GCD = 105"
] | null | null |
PGDP/printed/image/PGDP10K_new_77.png | printed | train | plane geometry | [
"R",
"T",
"S"
] | [
"line S R",
"line S T"
] | [
"\\odot S lieson T R"
] | [
"l \\widehat TR = 7.94",
"m \\angle TSR = 70"
] | null | null |
PGDP/printed/image/PGDP10K_new_78.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J"
] | [
"line A B C D",
"line B H G",
"line G E C",
"line J F C",
"line B I J",
"line G J",
"line H I",
"line E F"
] | [] | [] | null | null |
PGDP/printed/image/PGDP10K_new_79.png | printed | train | plane geometry | [
"C",
"B",
"D",
"A",
"E",
"F"
] | [
"line C E D",
"line A E B"
] | [
"\\odot F lieson C A D B"
] | [
"DE = 4",
"AE = x",
"CE = 3",
"BE = 6"
] | null | null |
PGDP/printed/image/PGDP10K_new_80.png | printed | train | plane geometry | [
"A",
"B",
"C"
] | [
"line A B",
"line B C",
"line A C"
] | [] | [
"m \\angle ABC = 117",
"m \\angle BCA = 33",
"m \\angle BAC = m \\angle 1"
] | null | null |
PGDP/printed/image/PGDP10K_new_81.png | printed | train | plane geometry | [
"A",
"D",
"E",
"F",
"C",
"B"
] | [
"line A F E",
"line E D",
"line C D",
"line F B C",
"line F D",
"line A B"
] | [] | [
"FC \\parallel ED",
"AE \\perp FC on F",
"CD \\perp FC on C",
"AE \\perp ED on E",
"m \\angle ABF = 48",
"m \\angle FDE = 39",
"m \\angle DFB = m \\angle 2",
"m \\angle FDC = m \\angle 3",
"m \\angle FAB = m \\angle 1"
] | null | null |
PGDP/printed/image/PGDP10K_new_83.png | printed | train | plane geometry | [
"P",
"A",
"B",
"C",
"D",
"E"
] | [
"line \\ell lieson D B C",
"line E P B A"
] | [] | [
"line \\ell \\perp EA on B"
] | null | null |
PGDP/printed/image/PGDP10K_new_84.png | printed | train | plane geometry | [
"P",
"M",
"L",
"N",
"A",
"B",
"C"
] | [
"line B M P",
"line M N",
"line L M",
"line A N P",
"line C L P"
] | [] | [
"LM \\perp CP on L",
"MN \\perp AP on N"
] | null | null |
PGDP/printed/image/PGDP10K_new_85.png | printed | train | plane geometry | [
"H",
"R",
"S",
"E",
"A"
] | [
"line H A S",
"line R S",
"line E S",
"line H E",
"line H R",
"line R A E"
] | [] | [
"RA = EA = 12",
"HA = 20",
"HR = HE",
"RS = ES"
] | null | null |
PGDP/printed/image/PGDP10K_new_86.png | printed | train | plane geometry | [
"M",
"P",
"O",
"Q",
"N"
] | [
"line P O",
"line Q N",
"line M Q P",
"line M N O"
] | [] | [
"QN \\parallel PO",
"PQ = x",
"ON = 3\\frac{3}{5}",
"MQ = 5",
"MN = 6"
] | null | null |
PGDP/printed/image/PGDP10K_new_87.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K"
] | [
"line I H G F D",
"line \\ell lieson J H A",
"line K G B",
"line m lieson E F C"
] | [] | [
"ID \\perp KB on G",
"m \\angle IHJ = 105",
"m \\angle GFC = 3x-18"
] | null | null |
PGDP/printed/image/PGDP10K_new_88.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"line A B",
"line B D",
"line D H",
"line F G H",
"line C F",
"line A C",
"line E G"
] | [] | [
"FH \\perp EG on G",
"EG = 8\\sqrt{3}"
] | null | null |
PGDP/printed/image/PGDP10K_new_89.png | printed | train | plane geometry | [
"A",
"D",
"C",
"B",
"E"
] | [
"line D E B",
"line A E C",
"line D A",
"line D C",
"line B C",
"line A B"
] | [] | [
"AE = 4",
"BE = 3"
] | null | null |
PGDP/printed/image/PGDP10K_new_90.png | printed | train | plane geometry | [
"H",
"M",
"G",
"J",
"K"
] | [
"line G K",
"line G H",
"line G M J",
"line H J K",
"line H M",
"line M K"
] | [] | [
"GJ \\perp HK on J",
"HJ = JK"
] | null | null |
PGDP/printed/image/PGDP10K_new_91.png | printed | train | plane geometry | [
"D",
"A",
"C",
"E",
"B"
] | [
"line C E",
"line D B E",
"line D A",
"line B A",
"line C B"
] | [] | [
"DB = BE",
"DA = CE",
"m \\angle BDA = 20",
"m \\angle CEB = 18"
] | null | null |
PGDP/printed/image/PGDP10K_new_92.png | printed | train | plane geometry | [
"S",
"X",
"P",
"T",
"Y",
"Q",
"Z"
] | [
"line S Q T",
"line Q Z",
"line P Z",
"line X P Y"
] | [
"\\odot Z lieson S X Y T"
] | [
"PZ \\perp XY on P",
"ST \\perp QZ on Q"
] | null | null |
PGDP/printed/image/PGDP10K_new_93.png | printed | train | plane geometry | [
"E",
"B",
"A",
"D",
"H",
"K",
"C",
"G",
"F",
"J"
] | [
"line A H D",
"line A E B",
"line B G C",
"line D K C",
"line J K",
"line H J",
"line E F",
"line F G"
] | [] | [
"m \\angle EBG = m \\angle 1",
"m \\angle EFG = m \\angle 2",
"m \\angle KJH = m \\angle 3",
"m \\angle HDK = m \\angle 4"
] | null | null |
PGDP/printed/image/PGDP10K_new_94.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"line A B",
"line B C",
"line C G",
"line F H G",
"line D F",
"line A D",
"line E H"
] | [] | [
"FG \\perp EH on H",
"BC = 42",
"EH = 36"
] | null | null |
PGDP/printed/image/PGDP10K_new_96.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D"
] | [
"line C B",
"line A B"
] | [
"\\odot D lieson A C"
] | [
"m \\angle CBA = 55",
"m major \\widehat CA = x"
] | null | null |
PGDP/printed/image/PGDP10K_new_97.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E"
] | [
"line A B",
"line B E",
"line D E",
"line A D",
"line A C E",
"line D C B"
] | [] | [
"AB \\perp AD on A",
"DE \\perp AD on D",
"BE \\perp DE on E",
"AB \\perp BE on B",
"m \\angle ABC = x",
"m \\angle ACB = y",
"m \\angle ECB = z",
"m \\angle EDC = 36"
] | null | null |
PGDP/printed/image/PGDP10K_new_98.png | printed | train | plane geometry | [
"P",
"Q",
"R",
"Z",
"Y",
"X",
"A"
] | [
"line P X A",
"line P Z R",
"line Q Y P",
"line Q A R",
"line Y X",
"line X Z"
] | [] | [
"QP \\perp YX on Y",
"PR \\perp XZ on Z"
] | null | null |
PGDP/printed/image/PGDP10K_new_99.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E"
] | [
"line A C D",
"line B C E"
] | [] | [
"m \\angle DCB = m \\angle 1",
"m \\angle ACB = m \\angle 4",
"m \\angle DCE = m \\angle 2",
"m \\angle ACE = m \\angle 3"
] | null | null |
PGDP/printed/image/PGDP10K_new_100.png | printed | train | plane geometry | [
"A",
"B",
"C"
] | [
"line C A",
"line A B",
"line C B"
] | [] | [
"AB \\perp CB on B",
"AB = 4",
"BC = 4\\sqrt{3}",
"CA = 8",
"m \\angle CAB = 60",
"m \\angle ACB = 30"
] | null | null |
PGDP/printed/image/PGDP10K_new_101.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H"
] | [
"line a lieson G F E",
"line b lieson B C D",
"line H F C A"
] | [] | [
"line a \\parallel line b",
"m \\angle GFH = m \\angle 1",
"m \\angle BCF = m \\angle 5",
"m \\angle DCA = m \\angle 7",
"m \\angle BCA = m \\angle 8"
] | null | null |
PGDP/printed/image/PGDP10K_new_103.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E"
] | [
"line A C",
"line A E",
"line C D E",
"line C B",
"line B D"
] | [] | [
"CE \\perp BD on D",
"AE = s",
"DC = \\frac{s}{2}"
] | null | null |
PGDP/printed/image/PGDP10K_new_105.png | printed | train | plane geometry | [
"C",
"W",
"X",
"Y",
"B",
"A",
"Z"
] | [
"line W X Y",
"line Y Z",
"line X A",
"line A Z",
"line X B",
"line C B",
"line W C"
] | [] | [] | null | null |
PGDP/printed/image/PGDP10K_new_106.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F"
] | [
"line A B F",
"line C A",
"line C D",
"line D F",
"line C B",
"line C E F",
"line D E"
] | [] | [
"CF \\perp DE on E",
"AF \\perp CB on B",
"AF = 21",
"DE = 4",
"CB = 6",
"CF = 18"
] | null | null |
PGDP/printed/image/PGDP10K_new_107.png | printed | train | plane geometry | [
"A",
"B",
"C"
] | [
"line A B",
"line C B",
"line C A"
] | [] | [
"AB \\perp CA on A",
"CA = x",
"AB = \\sqrt{2}",
"BC = x+1"
] | null | null |
PGDP/printed/image/PGDP10K_new_108.png | printed | train | plane geometry | [
"H",
"G",
"J",
"E",
"F"
] | [
"line G F E",
"line J E",
"line J F",
"line H F",
"line H G"
] | [] | [
"HF \\parallel JE",
"JF = HG",
"m \\angle EJF = m \\angle FHG"
] | null | null |
PGDP/printed/image/PGDP10K_new_110.png | printed | train | plane geometry | [
"A",
"B",
"C",
"D",
"E",
"F",
"G",
"H",
"I",
"J",
"K",
"L",
"M",
"N",
"O",
"P"
] | [
"line C D E F",
"line G H I J",
"line K L M N",
"line A D H L P",
"line B E I M O"
] | [] | [
"CF \\parallel GJ \\parallel KN",
"HL = 5x",
"DH = 4x",
"IE = 4x+8",
"MI = 6x-10"
] | null | null |
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