SunnyLin/FormalGeo7k_v1 huggingface dataset:
Problem: As shown in the diagram, ∠EAB=130°, ∠EDF=30°, AE∥BD. Find the measure of ∠BCD.
问题：如图所示，∠EAB=130°，∠EDF=30°，AE平行于BD。求∠BCD的大小。
Construction (CDL):
Shape(AB,BD,DE,EA)
Shape(BC,CD,DB)
Shape(ED,DF)
Collinear(BDF)
Collinear(ABC)
Collinear(EDC)
Conditions (CDL):
Equal(MeasureOfAngle(EAB),130)
Equal(MeasureOfAngle(EDF),30)
ParallelBetweenLine(AE,BD)
Goal: Value(MeasureOfAngle(BCD))
Answer: 20
Theorem sequence:
parallel_property_corresponding_angle(2,AE,BD,C)
vertical_angle(1,EDF,CDB)
triangle_property_angle_sum(1,BCD)
Problem: As shown in the diagram, ∠DBE=32°, DB bisects ∠EDA, AD∥BC. Find the measure of ∠DEC.
问题：如图所示，∠DBE=32°，DB平分∠EDA，AD平行于BC。求∠DEC的大小。
Construction (CDL):
Shape(DB,BE,ED)
Shape(BD,DA)
Shape(DE,EC)
Collinear(BEC)
Conditions (CDL):
Equal(MeasureOfAngle(DBE),32)
IsBisectorOfAngle(DB,EDA)
ParallelBetweenLine(AD,BC)
Goal: Value(MeasureOfAngle(DEC))
Answer: 64
Theorem sequence:
parallel_property_alternate_interior_angle(2,AD,BC)
angle_addition(1,EDB,BDA)
parallel_property_collinear_extend(3,CB,DA,E)
parallel_property_alternate_interior_angle(2,AD,EC)
Problem: As shown in the diagram, DE=DF, ∠ABD=40°, BA∥EC. Find the measure of ∠DEF.
问题：如图所示，DE=DF，∠ABD=40°，BA平行于EC。求∠DEF的大小。
Construction (CDL):
Shape(DE,EF,FD)
Shape(AB,BD)
Shape(BD,DC)
Shape(CD,DF)
Shape(ED,DB)
Collinear(BDF)
Collinear(CDE)
Conditions (CDL):
Equal(LengthOfLine(DE),LengthOfLine(DF))
Equal(MeasureOfAngle(ABD),40)
ParallelBetweenLine(BA,EC)
Goal: Value(MeasureOfAngle(DEF))
Answer: 20
Theorem sequence:
parallel_property_collinear_extend(3,CE,AB,D)
parallel_property_corresponding_angle(2,BA,DC,F)
flat_angle(1,CDE)
angle_addition(1,CDF,FDE)
isosceles_triangle_judgment_line_equal(1,DEF)
isosceles_triangle_property_angle_equal(1,DEF)
triangle_property_angle_sum(1,DEF)
Problem: As shown in the diagram, ∠EMN=40°, ABCD is a rectangle, ∠GEF is the right angle of the right triangle GEF. Find the measure of ∠GQP.
问题：如图所示，∠EMN=40°，四边形ABCD是长方形，∠GEF是直角三角形GEF的直角。求∠GQP的大小。
Construction (CDL):
Shape(EM,MN,NE)
Shape(AB,BP,PM,MA)
Shape(NQ,QC,CD,DN)
Shape(MP,PQ,QN,NM)
Shape(PF,FG,GQ,QP)
Collinear(AMND)
Collinear(BPQC)
Collinear(EMPF)
Collinear(ENQG)
Conditions (CDL):
Equal(MeasureOfAngle(EMN),40)
Rectangle(ABCD)
RightTriangle(GEF)
Goal: Value(MeasureOfAngle(GQP))
Answer: 130
Theorem sequence:
triangle_property_angle_sum(1,EMN)
parallel_property_collinear_extend(3,AD,BC,N)
parallel_property_collinear_extend(3,CB,NA,Q)
parallel_property_corresponding_angle(2,QB,NA,E)
flat_angle(1,GQN)
angle_addition(1,GQP,PQN)
Problem: As shown in the diagram, BC=1, MN=6, M is the midpoint of segment AB, N bisects segment CD. Find the length of line AD.
问题：如图所示，BC=1，MN=6，M是线段AB的中点，N是线段CD的中点。求直线AD的长度。
Construction (CDL):
Collinear(AMBCND)
Conditions (CDL):
Equal(LengthOfLine(BC),1)
Equal(LengthOfLine(MN),6)
IsMidpointOfLine(M,AB)
IsMidpointOfLine(N,CD)
Goal: Value(LengthOfLine(AD))
Answer: 11
Theorem sequence:
line_addition(1,AM,MB)
line_addition(1,AM,MN)
line_addition(1,AB,BC)
line_addition(1,AC,CN)
line_addition(1,AN,ND)
Problem: As shown in the diagram, ∠ABC=35°, AD is the angle bisector of ∠EAC, AD∥BC. Find the measure of ∠BCA.
问题：如图所示，∠ABC=35°，AD是∠EAC的角平分线，AD平行于BC。求∠BCA的大小。
Construction (CDL):
Shape(AB,BC,CA)
Shape(EA,AD)
Shape(DA,AC)
Shape(EA,AC)
Collinear(EAB)
Conditions (CDL):
Equal(MeasureOfAngle(ABC),35)
IsBisectorOfAngle(AD,EAC)
ParallelBetweenLine(AD,BC)
Goal: Value(MeasureOfAngle(BCA))
Answer: 35
Theorem sequence:
parallel_property_corresponding_angle(1,AD,BC,E)
parallel_property_alternate_interior_angle(1,AD,BC)
Problem: As shown in the diagram, ∠AOC=70°, OM bisects ∠AOC, MO is perpendicular to NO. Find the measure of ∠CON.
问题：如图所示，∠AOC=70°，OM平分∠AOC，MO⊥NO。求∠CON的大小。
Construction (CDL):
Shape(AO,OM)
Shape(MO,OC)
Shape(CO,ON)
Shape(NO,OB)
Shape(DO,OA)
Shape(BO,OD)
Shape(AO,OC)
Shape(MO,ON)
Shape(CO,OB)
Shape(AO,ON)
Shape(MO,OB)
Collinear(AOB)
Collinear(COD)
Conditions (CDL):
Equal(MeasureOfAngle(AOC),70)
IsBisectorOfAngle(OM,AOC)
PerpendicularBetweenLine(MO,NO)
Goal: Value(MeasureOfAngle(CON))
Answer: 55
Theorem sequence:
angle_addition(1,AOM,MOC)
angle_addition(1,MOC,CON)
Problem: As shown in the diagram, ∠GND=40°, ABCD is a rectangle, EF and FG are the legs of the right triangle EFG. Find the measure of ∠BFM.
问题：如图所示，∠GND=40°，ABCD是长方形，∠EFG是直角三角形EFG的直角。求∠BFM的大小。
Construction (CDL):
Shape(EM,MN,NG,GE)
Shape(AB,BF,FM,MA)
Shape(MF,FN,NM)
Shape(DN,NF,FC,CD)
Shape(GN,ND)
Shape(AM,ME)
Collinear(AMND)
Collinear(BFC)
Collinear(EMF)
Collinear(FNG)
Conditions (CDL):
Equal(MeasureOfAngle(GND),40)
Rectangle(ABCD)
RightTriangle(EFG)
Goal: Value(MeasureOfAngle(BFM))
Answer: 50
Theorem sequence:
parallel_property_collinear_extend(3,AD,BC,N)
parallel_property_collinear_extend(3,CB,DN,F)
parallel_property_corresponding_angle(1,ND,FC,G)
flat_angle(1,BFC)
angle_addition(1,BFM,MFN)
angle_addition(1,BFN,NFC)
Problem: As shown in the diagram, ∠GOE=40°, O is the center of ⊙O, EG⊥OG. Find the measure of ∠GDF.
问题：如图所示，∠GOE=40°，⊙O的圆心为O，EG垂直于OG。求∠GDF的大小。
Construction (CDL):
Shape(OCE,EO,OC)
Shape(OFC,CO,OF)
Shape(OE,EG,GO)
Shape(OG,GF,FO)
Shape(OED,DG,GE)
Shape(ODF,FD)
Shape(GD,DF,FG)
Shape(O)
Collinear(COGD)
Collinear(EGF)
Cocircular(O,CEDF)
Conditions (CDL):
Equal(MeasureOfAngle(GOE),40)
IsCentreOfCircle(O,O)
PerpendicularBetweenLine(EG,OG)
Goal: Value(MeasureOfAngle(GDF))
Answer: 70
Theorem sequence:
adjacent_complementary_angle(1,COF,FOG)
circle_property_chord_perpendicular_bisect_chord(1,O,OG,EF)
perpendicular_bisector_property_bisector(1,OG,EF)
arc_property_center_angle(1,OFC,O)
arc_property_circumference_angle_external(1,OFC,D)
Problem: As shown in the diagram, ∠OAD=25°, the center of ⊙O is O, the diameter of circle O is AB. Find the measure of ∠ECA.
问题：如图所示，∠OAD=25°，O是⊙O的圆心，AB是圆O的直径。求∠ECA的大小。
Construction (CDL):
Shape(OCA,AC)
Shape(OAD,DA)
Shape(ODB,BD)
Shape(OBC,CE,EB)
Shape(CA,AO,OE,EC)
Shape(AD,DE,EO,OA)
Shape(BE,ED,DB)
Collinear(AOEB)
Collinear(CED)
Cocircular(O,ADBC)
Conditions (CDL):
Equal(MeasureOfAngle(OAD),25)
IsCentreOfCircle(O,O)
IsDiameterOfCircle(AB,O)
Goal: Value(MeasureOfAngle(ECA))
Answer: 65
Theorem sequence:
triangle_property_angle_sum(1,ADB)
diameter_of_circle_property_right_angle(1,ADB,O)
arc_property_circumference_angle_external(1,OAD,B)
arc_property_circumference_angle_external(1,OAD,C)
Problem: As shown in the diagram, ∠PFQ=35°, ∠PMA=85°, AB∥CD. Find the measure of ∠NQD.
问题：如图所示，∠PFQ=35°，∠PMA=85°，AB∥CD。求∠NQD的大小。
Construction (CDL):
Shape(MP,PQ,QN,NM)
Shape(PF,FQ,QP)
Shape(AM,ME)
Shape(EM,MN)
Shape(MN,NG)
Shape(GN,NB)
Shape(PM,MA)
Shape(BN,NQ)
Shape(CP,PM)
Shape(NQ,QD)
Shape(FP,PC)
Shape(DQ,QF)
Collinear(AMNB)
Collinear(CPQD)
Collinear(EMPF)
Collinear(GNQF)
Conditions (CDL):
Equal(MeasureOfAngle(PFQ),35)
Equal(MeasureOfAngle(PMA),85)
ParallelBetweenLine(AB,CD)
Goal: Value(MeasureOfAngle(NQD))
Answer: 50
Theorem sequence:
flat_angle(1,NMA)
angle_addition(1,NMP,PMA)
triangle_property_angle_sum(1,MFN)
parallel_property_collinear_extend(3,AB,CD,N)
parallel_property_collinear_extend(3,DC,NA,Q)
parallel_property_alternate_interior_angle(2,DQ,NA)
Problem: As shown in the diagram, ∠COE=26°, AO⊥CO. Find the measure of ∠FOA.
问题：如图所示，∠COE=26°，AO⊥CO。求∠FOA的大小。
Construction (CDL):
Shape(AO,OC)
Shape(CO,OE)
Shape(EO,OB)
Shape(BO,OD)
Shape(DO,OF)
Shape(FO,OA)
Shape(AO,OE)
Shape(FO,OC)
Collinear(AOB)
Collinear(COD)
Collinear(EOF)
Conditions (CDL):
Equal(MeasureOfAngle(COE),26)
PerpendicularBetweenLine(AO,CO)
Goal: Value(MeasureOfAngle(FOA))
Answer: 64
Theorem sequence:
angle_addition(1,AOC,COE)
flat_angle(1,FOE)
angle_addition(1,FOA,AOE)
Problem: As shown in the diagram, ∠ABC=50°, CD∥AB, BC is perpendicular to AC. Find the measure of ∠ECD.
问题：如图所示，∠ABC=50°，CD∥AB，BC垂直于AC。求∠ECD的大小。
Construction (CDL):
Shape(CA,AB,BC)
Shape(EC,CD)
Shape(DC,CB)
Shape(EC,CB)
Collinear(ACE)
Conditions (CDL):
Equal(MeasureOfAngle(ABC),50)
ParallelBetweenLine(CD,AB)
PerpendicularBetweenLine(BC,AC)
Goal: Value(MeasureOfAngle(ECD))
Answer: 40
Theorem sequence:
adjacent_complementary_angle(1,ECB,BCA)
parallel_property_alternate_interior_angle(1,CD,AB)
angle_addition(1,ECD,DCB)
Problem: As shown in the diagram, Add(MeasureOfAngle(DOB)=MeasureOfAngle(COA)). Find the measure of ∠AOD.
问题：如图所示，Add(MeasureOfAngle(DOB)=MeasureOfAngle(COA))。求∠AOD的大小。
Construction (CDL):
Shape(CO,OA)
Shape(AO,OD)
Shape(BO,OC)
Shape(DO,OB)
Collinear(AOB)
Collinear(COD)
Conditions (CDL):
Equal(Add(MeasureOfAngle(DOB),MeasureOfAngle(COA)),100)
Goal: Value(MeasureOfAngle(AOD))
Answer: 130
Theorem sequence:
vertical_angle(1,COA,DOB)
flat_angle(1,COD)
angle_addition(1,COA,AOD)
Problem: As shown in the diagram, CB=CE, CD=CA, DE=58. Find the length of line AB.
问题：如图所示，CB=CE，CD=CA，DE=58。求直线AB的长度。
Construction (CDL):
Shape(AC,CB,BA)
Shape(CE,ED,DC)
Collinear(ACD)
Collinear(BCE)
Conditions (CDL):
Equal(LengthOfLine(CB),LengthOfLine(CE))
Equal(LengthOfLine(CD),LengthOfLine(CA))
Equal(LengthOfLine(DE),58)
Goal: Value(LengthOfLine(AB))
Answer: 58
Theorem sequence:
vertical_angle(1,ACB,DCE)
congruent_triangle_judgment_sas(1,CBA,CED)
congruent_triangle_property_line_equal(1,CBA,CED)
Problem: As shown in the diagram, ∠ECD=35°, ∠MEA=15°, ABCD is a parallelogram, EFGC is a square. Find the measure of ∠NBP.
问题：如图所示，∠ECD=35°，∠MEA=15°，AD和BC是平行四边形ABCD的一组对边，EFGC是正方形。求∠NBP的大小。
Construction (CDL):
Shape(AM,ME,EA)
Shape(MF,FN,NM)
Shape(NB,BP,PN)
Shape(MN,NP,PC,CE,EM)
Shape(DE,EC,CD)
Shape(PG,GC,CP)
Collinear(AED)
Collinear(BPC)
Collinear(AMNB)
Collinear(FME)
Collinear(FNPG)
Conditions (CDL):
Equal(MeasureOfAngle(ECD),35)
Equal(MeasureOfAngle(MEA),15)
Parallelogram(ABCD)
Square(EFGC)
Goal: Value(MeasureOfAngle(NBP))
Answer: 70
Theorem sequence:
angle_addition(1,CEM,MEA)
angle_addition(1,DEC,CEA)
flat_angle(1,DEA)
triangle_property_angle_sum(1,DEC)
parallelogram_property_opposite_angle_equal(1,BCDA)
Problem: As shown in the diagram, ∠EDC=40°, CD is the angle bisector of ∠BCE, DE∥BC. Find the measure of ∠DEA.
问题：如图所示，∠EDC=40°，CD是∠BCE的角平分线，DE∥BC。求∠DEA的大小。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CD)
Shape(ED,DC,CE)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(MeasureOfAngle(EDC),40)
IsBisectorOfAngle(CD,BCE)
ParallelBetweenLine(DE,BC)
Goal: Value(MeasureOfAngle(DEA))
Answer: 80
Theorem sequence:
parallel_property_alternate_interior_angle(1,DE,BC)
angle_addition(1,BCD,DCE)
parallel_property_corresponding_angle(2,CB,ED,A)
Problem: As shown in the diagram, ∠EMB=68°, AB is parallel to CD. Find the measure of ∠CNM.
问题：如图所示，∠EMB=68°，AB平行于CD。求∠CNM的大小。
Construction (CDL):
Shape(AM,ME)
Shape(EM,MB)
Shape(NM,MA)
Shape(BM,MN)
Shape(CN,NM)
Shape(MN,ND)
Shape(FN,NC)
Shape(DN,NF)
Collinear(AMB)
Collinear(CND)
Collinear(EMNF)
Conditions (CDL):
Equal(MeasureOfAngle(EMB),68)
ParallelBetweenLine(AB,CD)
Goal: Value(MeasureOfAngle(CNM))
Answer: 112
Theorem sequence:
parallel_property_collinear_extend(3,AB,CD,M)
parallel_property_collinear_extend(3,DC,BM,N)
parallel_property_corresponding_angle(1,MB,ND,E)
flat_angle(1,CND)
angle_addition(1,CNM,MND)
Problem: As shown in the diagram, ∠CBA=46°, ∠FEC=154°, AB is parallel to CD, AB∥EF, EF is parallel to CD. Find the measure of ∠BCE.
问题：如图所示，∠CBA=46°，∠FEC=154°，AB平行于CD，AB∥EF，EF∥CD。求∠BCE的大小。
Construction (CDL):
Shape(BC,CE,EF,FB)
Shape(EC,CD,DF,FE)
Shape(CB,BA)
Shape(FB,BA)
Conditions (CDL):
Equal(MeasureOfAngle(CBA),46)
Equal(MeasureOfAngle(FEC),154)
ParallelBetweenLine(AB,CD)
ParallelBetweenLine(AB,EF)
ParallelBetweenLine(EF,CD)
Goal: Value(MeasureOfAngle(BCE))
Answer: 20
Theorem sequence:
parallel_property_alternate_interior_angle(2,AB,CD)
parallel_property_ipsilateral_internal_angle(1,EF,CD)
angle_addition(1,BCE,ECD)
Problem: As shown in the diagram, ∠DAE=40°, ∠ECB=90°, the center of ⊙C is C. Find the measure of ∠ECD.
问题：如图所示，∠DAE=40°，∠ECB=90°，C是圆C的圆心。求∠ECD的大小。
Construction (CDL):
Shape(CEB,BC,CE)
Shape(CBD,DB)
Shape(CDE,EC,CD)
Shape(CDE,DA,AE)
Shape(CB,BD,DC)
Collinear(AEC)
Collinear(ADB)
Cocircular(C,BDE)
Conditions (CDL):
Equal(MeasureOfAngle(DAE),40)
Equal(MeasureOfAngle(ECB),90)
IsCentreOfCircle(C,C)
Goal: Value(MeasureOfAngle(ECD))
Answer: 10
Theorem sequence:
triangle_property_angle_sum(1,ACB)
radius_of_circle_property_length_equal(1,CB,C)
radius_of_circle_property_length_equal(1,CD,C)
isosceles_triangle_judgment_line_equal(1,CBD)
isosceles_triangle_property_angle_equal(1,CBD)
triangle_property_angle_sum(1,DCB)
angle_addition(1,ACD,DCB)
Problem: As shown in the diagram, ∠EDA=36°, O is the center of circle O, AB is the diameter of circle O. Find the measure of ∠EAC.
问题：如图所示，∠EDA=36°，⊙O的圆心为O，圆O的直径为AB。求∠EAC的大小。
Construction (CDL):
Shape(OCB,BC)
Shape(OAC,CA)
Shape(OBD,DE,EO,OB)
Shape(ODA,AE,ED)
Shape(CB,BO,OE,EC)
Shape(CE,EA,AC)
Shape(ED,DA,AE)
Collinear(BOEA)
Collinear(CED)
Cocircular(O,ACBD)
Conditions (CDL):
Equal(MeasureOfAngle(EDA),36)
IsCentreOfCircle(O,O)
IsDiameterOfCircle(AB,O)
Goal: Value(MeasureOfAngle(EAC))
Answer: 54
Theorem sequence:
diameter_of_circle_property_right_angle(1,ACB,O)
arc_property_circumference_angle_external(1,OAC,B)
arc_property_circumference_angle_external(1,OAC,D)
triangle_property_angle_sum(1,CBA)
Problem: As shown in the diagram, ∠DAC=100°, triangle DAC is mirror congruent to triangle DCE. Find the measure of ∠DBC.
问题：如图所示，∠DAC=100°，△DAC与△DCE是镜像全等三角形。求∠DBC的大小。
Construction (CDL):
Shape(ODB,BD)
Shape(OBC,CB)
Shape(OCE,EC)
Shape(OED,DE)
Shape(AD,DB,BC,CA)
Shape(AC,CD,DA)
Shape(CE,ED,DC)
Shape(O)
Cocircular(O,BCED)
Conditions (CDL):
Equal(MeasureOfAngle(DAC),100)
MirrorCongruentBetweenTriangle(DAC,DCE)
Goal: Value(MeasureOfAngle(DBC))
Answer: 80
Theorem sequence:
mirror_congruent_triangle_property_angle_equal(1,ACD,EDC)
arc_property_circumference_angle_external(1,ODC,E)
arc_property_circumference_angle_internal(1,ODC,B)
Problem: As shown in the diagram, ∠BPC=20°, O is the center of ⊙O, PC is the tangent to circle O. Find the measure of ∠CAO.
问题：如图所示，∠BPC=20°，O是⊙O的圆心，PC是⊙O的切线。求∠CAO的大小。
Construction (CDL):
Shape(OCA,AC)
Shape(OAB,BO,OA)
Shape(OBC,CO,OB)
Shape(OBC,BP,PC)
Shape(CA,AO,OC)
Collinear(AOBP)
Cocircular(O,ABC)
Conditions (CDL):
Equal(MeasureOfAngle(BPC),20)
IsCentreOfCircle(O,O)
IsTangentOfCircle(PC,O)
Goal: Value(MeasureOfAngle(CAO))
Answer: 35
Theorem sequence:
tangent_of_circle_property_perpendicular(2,PC,O,O)
triangle_property_angle_sum(1,COP)
arc_property_center_angle(1,OBC,O)
arc_property_circumference_angle_external(1,OBC,A)
Problem: As shown in the diagram, ∠CFM=70°, BA is parallel to DC. Find the measure of ∠FEB.
问题：如图所示，∠CFM=70°，BA平行于DC。求∠FEB的大小。
Construction (CDL):
Shape(CF,FM)
Shape(MF,FD)
Shape(EF,FC)
Shape(DF,FE)
Shape(AE,EF)
Shape(FE,EB)
Shape(NE,EA)
Shape(BE,EN)
Collinear(CFD)
Collinear(AEB)
Collinear(MFEN)
Conditions (CDL):
Equal(MeasureOfAngle(CFM),70)
ParallelBetweenLine(BA,DC)
Goal: Value(MeasureOfAngle(FEB))
Answer: 110
Theorem sequence:
parallel_property_collinear_extend(3,BA,DC,E)
parallel_property_collinear_extend(3,CD,AE,F)
parallel_property_corresponding_angle(2,EA,FC,M)
flat_angle(1,AEB)
angle_addition(1,AEF,FEB)
Problem: As shown in the diagram, ∠EMN=60°, ∠FNM=70°, ∠MEA=40°, AB is parallel to CD, AB is parallel to GH, GH is parallel to PQ, PQ is parallel to CD. Find the measure of ∠NFD.
问题：如图所示，∠EMN=60°，∠FNM=70°，∠MEA=40°，AB平行于CD，AB平行于GH，GH平行于PQ，PQ∥CD。求∠NFD的大小。
Construction (CDL):
Shape(ME,EA)
Shape(BE,EM)
Shape(GM,ME)
Shape(EM,MH)
Shape(NM,MG)
Shape(HM,MN)
Shape(PN,NM)
Shape(MN,NQ)
Shape(FN,NP)
Shape(QN,NF)
Shape(CF,FN)
Shape(NF,FD)
Collinear(AEB)
Collinear(GMH)
Collinear(PNQ)
Collinear(CFD)
Conditions (CDL):
Equal(MeasureOfAngle(EMN),60)
Equal(MeasureOfAngle(FNM),70)
Equal(MeasureOfAngle(MEA),40)
ParallelBetweenLine(AB,CD)
ParallelBetweenLine(AB,GH)
ParallelBetweenLine(GH,PQ)
ParallelBetweenLine(PQ,CD)
Goal: Value(MeasureOfAngle(NFD))
Answer: 50
Theorem sequence:
parallel_property_collinear_extend(3,AB,GH,E)
parallel_property_collinear_extend(3,GH,PQ,M)
parallel_property_collinear_extend(3,PQ,CD,N)
parallel_property_collinear_extend(3,HG,EA,M)
parallel_property_collinear_extend(3,QP,HM,N)
parallel_property_collinear_extend(3,DC,NP,F)
parallel_property_alternate_interior_angle(1,NP,HM)
parallel_property_alternate_interior_angle(2,HM,EA)
parallel_property_alternate_interior_angle(2,DF,NP)
angle_addition(1,EMH,HMN)
angle_addition(1,FNP,PNM)
Problem: As shown in the diagram, DE=1100, D is the midpoint of segment AC, E bisects segment BC. Find the length of line AB.
问题：如图所示，DE=1100，D平分线段AC，E是线段BC的中点。求直线AB的长度。
Construction (CDL):
Shape(AD,DE,EB,BA)
Shape(DC,CE,ED)
Collinear(ADC)
Collinear(BEC)
Conditions (CDL):
Equal(LengthOfLine(DE),1100)
IsMidpointOfLine(D,AC)
IsMidpointOfLine(E,BC)
Goal: Value(LengthOfLine(AB))
Answer: 2200
Theorem sequence:
midsegment_of_triangle_judgment_midpoint(1,ED,CBA)
midsegment_of_triangle_property_length(1,ED,CBA)
Problem: As shown in the diagram, ∠DCG=50°, ∠FAG=30°, quadrilateral EDCF is a rectangle, CB and BA are the legs of the right triangle CBA. Find the measure of ∠GFA.
问题：如图所示，∠DCG=50°，∠FAG=30°，EDCF是长方形，三角形CBA为直角三角形。求∠GFA的大小。
Construction (CDL):
Shape(FA,AG,GF)
Shape(FG,GC,CF)
Shape(BF,FC,CB)
Shape(GE,ED,DC,CG)
Collinear(EGF)
Collinear(AGC)
Collinear(AFB)
Conditions (CDL):
Equal(MeasureOfAngle(DCG),50)
Equal(MeasureOfAngle(FAG),30)
Rectangle(EDCF)
RightTriangle(CBA)
Goal: Value(MeasureOfAngle(GFA))
Answer: 20
Theorem sequence:
parallel_property_collinear_extend(3,EF,DC,G)
parallel_property_alternate_interior_angle(1,GF,DC)
flat_angle(1,AGC)
angle_addition(1,AGF,FGC)
triangle_property_angle_sum(1,AGF)
Problem: As shown in the diagram, ∠CAB=50°, O is the center of ⊙O. Find the measure of ∠OBC.
问题：如图所示，∠CAB=50°，⊙O的圆心为O。求∠OBC的大小。
Construction (CDL):
Shape(OCA,AC)
Shape(OAB,BA)
Shape(OBC,CB)
Shape(CA,AB,BO,OC)
Shape(OB,BC,CO)
Cocircular(O,ABC)
Conditions (CDL):
Equal(MeasureOfAngle(CAB),50)
IsCentreOfCircle(O,O)
Goal: Value(MeasureOfAngle(OBC))
Answer: 40
Theorem sequence:
arc_property_circumference_angle_external(1,OBC,A)
arc_property_center_angle(1,OBC,O)
radius_of_circle_property_length_equal(1,OB,O)
radius_of_circle_property_length_equal(1,OC,O)
isosceles_triangle_judgment_line_equal(1,OBC)
isosceles_triangle_property_angle_equal(1,OBC)
triangle_property_angle_sum(1,OBC)
Problem: As shown in the diagram, ∠CAB=110°, D is the center of ⊙D, the circumcenter of quadrilateral ABCD is O. Find the measure of ∠BDC.
问题：如图所示，∠CAB=110°，D是圆D的圆心，O是四边形ABCD外切圆的圆心。求∠BDC的大小。
Construction (CDL):
Shape(DCA,AC)
Shape(DAB,BA)
Shape(DBE,EB)
Shape(DEC,CE)
Shape(DC,CA,AB,BD)
Shape(DB,BE,EC,CD)
Cocircular(D,ABEC)
Conditions (CDL):
Equal(MeasureOfAngle(CAB),110)
IsCentreOfCircle(D,D)
IsCircumcenterOfQuadrilateral(O,ABCD)
Goal: Value(MeasureOfAngle(BDC))
Answer: 140
Theorem sequence:
arc_property_circumference_angle_internal(1,DCB,A)
arc_property_center_angle(1,DCB,D)
Problem: As shown in the diagram, ∠EGB=50°, AB∥CD. Find the measure of ∠CHG.
问题：如图所示，∠EGB=50°，AB平行于CD。求∠CHG的大小。
Construction (CDL):
Shape(AG,GE)
Shape(EG,GB)
Shape(HG,GA)
Shape(BG,GH)
Shape(CH,HG)
Shape(GH,HD)
Shape(FH,HC)
Shape(DH,HF)
Collinear(AGB)
Collinear(CHD)
Collinear(EGHF)
Conditions (CDL):
Equal(MeasureOfAngle(EGB),50)
ParallelBetweenLine(AB,CD)
Goal: Value(MeasureOfAngle(CHG))
Answer: 130
Theorem sequence:
parallel_property_collinear_extend(3,AB,CD,G)
parallel_property_collinear_extend(3,DC,BG,H)
parallel_property_corresponding_angle(1,GB,HD,E)
flat_angle(1,CHD)
angle_addition(1,CHG,GHD)
Problem: As shown in the diagram, ∠AGF=60°. Find the sum of the measure of ∠FAG, the measure of ∠MBP, the measure of ∠PCH, the measure of ∠HDQ, the measure of ∠QEN and the measure of ∠GFA.
问题：如图所示，∠AGF=60°。求∠FAG的大小、∠MBP的大小、∠PCH的大小、∠HDQ的大小、∠QEN的大小与∠GFA的大小之和。
Construction (CDL):
Shape(FA,AG,GF)
Shape(GM,MN,NG)
Shape(MB,BP,PM)
Shape(EN,NQ,QE)
Shape(NM,MP,PH,HQ,QN)
Shape(PC,CH,HP)
Shape(QH,HD,DQ)
Collinear(AGNQD)
Collinear(FGMPC)
Collinear(BPHD)
Collinear(BMNE)
Collinear(CHQE)
Conditions (CDL):
Equal(MeasureOfAngle(AGF),60)
Goal: Value(Add(MeasureOfAngle(FAG),MeasureOfAngle(MBP),MeasureOfAngle(PCH),MeasureOfAngle(HDQ),MeasureOfAngle(QEN),MeasureOfAngle(GFA)))
Answer: 240
Theorem sequence:
triangle_property_angle_sum(1,BHE)
flat_angle(1,PHD)
angle_addition(1,PHQ,QHD)
triangle_property_angle_sum(1,GCQ)
flat_angle(1,DQN)
angle_addition(1,DQH,HQN)
triangle_property_angle_sum(1,DQH)
vertical_angle(1,AGF,NGM)
triangle_property_angle_sum(1,AGF)
Problem: As shown in the diagram, AB=3, BC=4, AB⊥CB. Find the sum of the length of line AB and the length of line AC.
问题：如图所示，AB=3，BC=4，AB⊥CB。求直线AB的长度与直线AC的长度之和。
Construction (CDL):
Shape(AB,BC,CA)
Conditions (CDL):
Equal(LengthOfLine(AB),3)
Equal(LengthOfLine(BC),4)
PerpendicularBetweenLine(AB,CB)
Goal: Value(Add(LengthOfLine(AB),LengthOfLine(AC)))
Answer: 8
Theorem sequence:
right_triangle_judgment_angle(1,ABC)
right_triangle_property_pythagorean(1,ABC)
Problem: As shown in the diagram, ∠NFD=130°, BA is parallel to DC, ME is perpendicular to HE. Find the measure of ∠HEA.
问题：如图所示，∠NFD=130°，BA平行于DC，ME垂直于HE。求∠HEA的大小。
Construction (CDL):
Shape(ME,EH)
Shape(HE,EA)
Shape(AE,EF)
Shape(HE,EF)
Shape(EF,FC)
Shape(CF,FN)
Shape(BE,EM)
Shape(FE,EB)
Shape(DF,FE)
Shape(NF,FD)
Collinear(MEFN)
Collinear(AEB)
Collinear(CFD)
Conditions (CDL):
Equal(MeasureOfAngle(NFD),130)
ParallelBetweenLine(BA,DC)
PerpendicularBetweenLine(ME,HE)
Goal: Value(MeasureOfAngle(HEA))
Answer: 40
Theorem sequence:
vertical_angle(1,MFC,NFD)
parallel_property_collinear_extend(3,BA,DC,E)
parallel_property_collinear_extend(3,CD,AE,F)
parallel_property_ipsilateral_internal_angle(1,EA,FC)
adjacent_complementary_angle(1,MEH,HEF)
angle_addition(1,HEA,AEF)
Problem: As shown in the diagram, BC=4, ∠ACB=90°, ∠DAC=30°, D bisects segment AB. Find the length of line CD.
问题：如图所示，BC=4，∠ACB=90°，∠DAC=30°，D平分线段AB。求直线CD的长度。
Construction (CDL):
Shape(DA,AC,CD)
Shape(CB,BD,DC)
Collinear(ADB)
Conditions (CDL):
Equal(LengthOfLine(BC),4)
Equal(MeasureOfAngle(ACB),90)
Equal(MeasureOfAngle(DAC),30)
IsMidpointOfLine(D,AB)
Goal: Value(LengthOfLine(CD))
Answer: 4
Theorem sequence:
sine_theorem(1,BAC)
line_addition(1,AD,DB)
isosceles_triangle_judgment_line_equal(1,BDC)
isosceles_triangle_property_angle_equal(1,BDC)
triangle_property_angle_sum(1,BAC)
triangle_property_angle_sum(1,BDC)
sine_theorem(1,DCB)
Problem: As shown in the diagram, ∠FEA=115°, EABF is mirror congruent to EFGH, quadrilateral ABCD is a rectangle. Find the measure of ∠GFC.
问题：如图所示，∠FEA=115°，EABF镜像全等于EFGH，四边形ABCD是矩形。求∠GFC的大小。
Construction (CDL):
Shape(EA,AB,BF,FE)
Shape(HE,EP,PH)
Shape(DP,PG,GF,FC,CD)
Shape(PE,EF,FG,GP)
Collinear(AEPD)
Collinear(BFC)
Collinear(HPG)
Conditions (CDL):
Equal(MeasureOfAngle(FEA),115)
MirrorCongruentBetweenQuadrilateral(EABF,EFGH)
Rectangle(ABCD)
Goal: Value(MeasureOfAngle(GFC))
Answer: 50
Theorem sequence:
mirror_congruent_quadrilateral_property_angle_equal(1,EABF,EFGH)
mirror_congruent_quadrilateral_property_angle_equal(1,ABFE,HEFG)
mirror_congruent_quadrilateral_property_angle_equal(1,BFEA,GHEF)
parallel_judgment_ipsilateral_internal_angle(1,AE,BF)
parallel_judgment_ipsilateral_internal_angle(1,GF,HE)
parallel_property_ipsilateral_internal_angle(1,FB,EA)
parallel_property_ipsilateral_internal_angle(1,EH,FG)
angle_addition(1,BFE,EFG)
flat_angle(1,BFC)
angle_addition(1,BFG,GFC)
Problem: As shown in the diagram, ∠CNM=120°, ∠EMP=60°, ∠QPM=125°. Find the measure of ∠HQN.
问题：如图所示，∠CNM=120°，∠EMP=60°，∠QPM=125°。求∠HQN的大小。
Construction (CDL):
Shape(MN,NQ,QP,PM)
Shape(AM,ME)
Shape(EM,MP)
Shape(MP,PG)
Shape(GP,PB)
Shape(NM,MA)
Shape(PM,MN)
Shape(QP,PM)
Shape(BP,PQ)
Shape(CN,NM)
Shape(MN,NQ)
Shape(NQ,QP)
Shape(PQ,QD)
Shape(FN,NC)
Shape(QN,NF)
Shape(HQ,QN)
Shape(DQ,QH)
Collinear(AMPB)
Collinear(CNQD)
Collinear(EMNF)
Collinear(GPQH)
Conditions (CDL):
Equal(MeasureOfAngle(CNM),120)
Equal(MeasureOfAngle(EMP),60)
Equal(MeasureOfAngle(QPM),125)
Goal: Value(MeasureOfAngle(HQN))
Answer: 125
Theorem sequence:
flat_angle(1,CNQ)
angle_addition(1,CNM,MNQ)
parallel_judgment_corresponding_angle(1,MP,NQ,E)
parallel_property_corresponding_angle(1,QN,PM,H)