SunnyLin/FormalGeo7k_v1 huggingface dataset:
Problem: As shown in the diagram, Div(LengthOfLine(AD)=LengthOfLine(BD)), DE=4, DE is parallel to BC. Find the length of line BC.
问题：如图所示，Div(LengthOfLine(AD)=LengthOfLine(BD))，DE=4，DE∥BC。求直线BC的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(Div(LengthOfLine(AD),LengthOfLine(BD)),1/2)
Equal(LengthOfLine(DE),4)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(BC))
Answer: 12
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,ADE,ABC)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AD,DB)
Problem: As shown in the diagram, AD=5, AE=3, BD=10, DE∥BC. Find the length of line AC.
问题：如图所示，AD=5，AE=3，BD=10，DE平行于BC。求直线AC的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(LengthOfLine(AD),5)
Equal(LengthOfLine(AE),3)
Equal(LengthOfLine(BD),10)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(AC))
Answer: 9
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,DEA,BCA)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AD,DB)
Problem: As shown in the diagram, Div(LengthOfLine(AD)=LengthOfLine(BD)), DE∥BC. Find the ratio of the length of line AE to the length of line EC.
问题：如图所示，Div(LengthOfLine(AD)=LengthOfLine(BD))，DE平行于BC。求直线AE的长度与直线EC的长度之比。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(Div(LengthOfLine(AD),LengthOfLine(BD)),2/3)
ParallelBetweenLine(DE,BC)
Goal: Value(Div(LengthOfLine(AE),LengthOfLine(EC)))
Answer: 2/3
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ABC,ADE)
similar_triangle_property_line_ratio(1,BCA,DEA)
similar_triangle_property_line_ratio(1,CAB,EAD)
line_addition(1,AD,DB)
line_addition(1,AE,EC)
Problem: As shown in the diagram, AD=4, AE=3, DB=6, DE is parallel to BC. Find the length of line AC.
问题：如图所示，AD=4，AE=3，DB=6，DE∥BC。求直线AC的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(LengthOfLine(AD),4)
Equal(LengthOfLine(AE),3)
Equal(LengthOfLine(DB),6)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(AC))
Answer: 15/2
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,DEA,BCA)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AD,DB)
Problem: As shown in the diagram, Div(LengthOfLine(AD)=LengthOfLine(BD)), DE=4, DE∥BC. Find the length of line BC.
问题：如图所示，Div(LengthOfLine(AD)=LengthOfLine(BD))，DE=4，DE平行于BC。求直线BC的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(Div(LengthOfLine(AD),LengthOfLine(BD)),1/2)
Equal(LengthOfLine(DE),4)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(BC))
Answer: 12
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,ADE,ABC)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AD,DB)
Problem: As shown in the diagram, AD=5, BD=10, DE=4, DE is parallel to BC. Find the length of line BC.
问题：如图所示，AD=5，BD=10，DE=4，DE∥BC。求直线BC的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(LengthOfLine(AD),5)
Equal(LengthOfLine(BD),10)
Equal(LengthOfLine(DE),4)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(BC))
Answer: 12
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,ADE,ABC)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AD,DB)
Problem: As shown in the diagram, AB=1, BC=2, DE=3/2, AD∥BE, AD is parallel to CF, BE is parallel to CF. Find the length of line EF.
问题：如图所示，AB=1，BC=2，DE=3/2，AD∥BE，AD平行于CF，BE平行于CF。求直线EF的长度。
Construction (CDL):
Shape(MA,AD,DM)
Shape(AB,BE,ED,DA)
Shape(BC,CF,FE,EB)
Collinear(MABC)
Collinear(MDEF)
Conditions (CDL):
Equal(LengthOfLine(AB),1)
Equal(LengthOfLine(BC),2)
Equal(LengthOfLine(DE),3/2)
ParallelBetweenLine(AD,BE)
ParallelBetweenLine(AD,CF)
ParallelBetweenLine(BE,CF)
Goal: Value(LengthOfLine(EF))
Answer: 3
Theorem sequence:
parallel_property_corresponding_angle(1,AD,BE,M)
parallel_property_corresponding_angle(1,AD,CF,M)
parallel_property_corresponding_angle(2,EB,DA,M)
parallel_property_corresponding_angle(2,FC,DA,M)
similar_triangle_judgment_aa(1,MAD,MBE)
similar_triangle_judgment_aa(1,MAD,MCF)
similar_triangle_property_line_ratio(1,ADM,BEM)
similar_triangle_property_line_ratio(1,DMA,EMB)
similar_triangle_property_line_ratio(1,ADM,CFM)
similar_triangle_property_line_ratio(1,DMA,FMC)
line_addition(1,MA,AB)
line_addition(1,MB,BC)
line_addition(1,MD,DE)
line_addition(1,ME,EF)
Problem: As shown in the diagram, Div(LengthOfLine(AD)=LengthOfLine(BD)), AE=4, DE is parallel to BC. Find the length of line AC.
问题：如图所示，Div(LengthOfLine(AD)=LengthOfLine(BD))，AE=4，DE∥BC。求直线AC的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(Div(LengthOfLine(AD),LengthOfLine(BD)),1/2)
Equal(LengthOfLine(AE),4)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(AC))
Answer: 12
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,DEA,BCA)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AD,DB)
Problem: As shown in the diagram, AC=4, BD=3, CE=6, AB is parallel to CD, AB∥EF, CD∥EF. Find the length of line BF.
问题：如图所示，AC=4，BD=3，CE=6，AB∥CD，AB∥EF，CD∥EF。求直线BF的长度。
Construction (CDL):
Shape(MA,AB,BM)
Shape(AC,CD,DB,BA)
Shape(CE,EF,FD,DC)
Collinear(MACE)
Collinear(MBDF)
Conditions (CDL):
Equal(LengthOfLine(AC),4)
Equal(LengthOfLine(BD),3)
Equal(LengthOfLine(CE),6)
ParallelBetweenLine(AB,CD)
ParallelBetweenLine(AB,EF)
ParallelBetweenLine(CD,EF)
Goal: Value(LengthOfLine(BF))
Answer: 15/2
Theorem sequence:
parallel_property_corresponding_angle(1,AB,CD,M)
parallel_property_corresponding_angle(1,AB,EF,M)
parallel_property_corresponding_angle(2,DC,BA,M)
parallel_property_corresponding_angle(2,FE,BA,M)
similar_triangle_judgment_aa(1,MAB,MCD)
similar_triangle_judgment_aa(1,MAB,MEF)
similar_triangle_property_line_ratio(1,ABM,CDM)
similar_triangle_property_line_ratio(1,BMA,DMC)
similar_triangle_property_line_ratio(1,ABM,EFM)
similar_triangle_property_line_ratio(1,BMA,FME)
line_addition(1,MA,AC)
line_addition(1,MC,CE)
line_addition(1,MB,BD)
line_addition(1,MB,BF)
Problem: As shown in the diagram, AC=3, BD=2, CE=6, AB∥CD, AB is parallel to EF, CD∥EF. Find the length of line DF.
问题：如图所示，AC=3，BD=2，CE=6，AB∥CD，AB平行于EF，CD∥EF。求直线DF的长度。
Construction (CDL):
Shape(MA,AB,BM)
Shape(AC,CD,DB,BA)
Shape(CE,EF,FD,DC)
Collinear(MACE)
Collinear(MBDF)
Conditions (CDL):
Equal(LengthOfLine(AC),3)
Equal(LengthOfLine(BD),2)
Equal(LengthOfLine(CE),6)
ParallelBetweenLine(AB,CD)
ParallelBetweenLine(AB,EF)
ParallelBetweenLine(CD,EF)
Goal: Value(LengthOfLine(DF))
Answer: 4
Theorem sequence:
parallel_property_corresponding_angle(1,AB,CD,M)
parallel_property_corresponding_angle(1,AB,EF,M)
parallel_property_corresponding_angle(2,DC,BA,M)
parallel_property_corresponding_angle(2,FE,BA,M)
similar_triangle_judgment_aa(1,MAB,MCD)
similar_triangle_judgment_aa(1,MAB,MEF)
similar_triangle_property_line_ratio(1,ABM,CDM)
similar_triangle_property_line_ratio(1,BMA,DMC)
similar_triangle_property_line_ratio(1,ABM,EFM)
similar_triangle_property_line_ratio(1,BMA,FME)
line_addition(1,MA,AC)
line_addition(1,MC,CE)
line_addition(1,MB,BD)
line_addition(1,MD,DF)
Problem: As shown in the diagram, AD=4, DB=6, DE=2, DE∥BC. Find the length of line BC.
问题：如图所示，AD=4，DB=6，DE=2，DE平行于BC。求直线BC的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(LengthOfLine(AD),4)
Equal(LengthOfLine(DB),6)
Equal(LengthOfLine(DE),2)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(BC))
Answer: 5
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,ADE,ABC)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AD,DB)
Problem: As shown in the diagram, Div(LengthOfLine(AD)=LengthOfLine(DB)), EC=6, DE is parallel to BC. Find the length of line AE.
问题：如图所示，Div(LengthOfLine(AD)=LengthOfLine(DB))，EC=6，DE平行于BC。求直线AE的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(Div(LengthOfLine(AD),LengthOfLine(DB)),2/3)
Equal(LengthOfLine(EC),6)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(AE))
Answer: 4
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,DEA,BCA)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AD,DB)
line_addition(1,AE,EC)
Problem: As shown in the diagram, EF=4, Mul(LengthOfLine(DE)=2), EF∥AB, DABC is a parallelogram. Find the length of line CD.
问题：如图所示，EF=4，Mul(LengthOfLine(DE)=2)，EF平行于AB，AD和BC是平行四边形DABC的一组对边。求直线CD的长度。
Construction (CDL):
Shape(DE,EF,FD)
Shape(EA,AB,BF,FE)
Shape(DF,FB,BC,CD)
Collinear(DEA)
Collinear(DFB)
Conditions (CDL):
Equal(LengthOfLine(EF),4)
Equal(Mul(LengthOfLine(DE),2),LengthOfLine(EA))
ParallelBetweenLine(EF,AB)
Parallelogram(DABC)
Goal: Value(LengthOfLine(CD))
Answer: 12
Theorem sequence:
parallel_property_corresponding_angle(1,EF,AB,D)
parallel_property_corresponding_angle(2,BA,FE,D)
similar_triangle_judgment_aa(1,DEF,DAB)
similar_triangle_property_line_ratio(1,DEF,DAB)
similar_triangle_property_line_ratio(1,FDE,BDA)
line_addition(1,DE,EA)
parallelogram_property_opposite_line_equal(1,ABCD)
Problem: As shown in the diagram, Div(LengthOfLine(AD)=LengthOfLine(DB)), DE=6, DE∥BC. Find the length of line BC.
问题：如图所示，Div(LengthOfLine(AD)=LengthOfLine(DB))，DE=6，DE平行于BC。求直线BC的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(Div(LengthOfLine(AD),LengthOfLine(DB)),3/5)
Equal(LengthOfLine(DE),6)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(BC))
Answer: 16
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,ADE,ABC)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AD,DB)
Problem: As shown in the diagram, AB=9/2, BC=3, EF=2, AD is parallel to EB, AD∥FC, EB is parallel to FC. Find the length of line DE.
问题：如图所示，AB=9/2，BC=3，EF=2，AD平行于EB，AD平行于FC，EB平行于FC。求直线DE的长度。
Construction (CDL):
Shape(AM,MD,DA)
Shape(ME,EB,BM)
Shape(EF,FC,CB,BE)
Collinear(AMBC)
Collinear(DMEF)
Conditions (CDL):
Equal(LengthOfLine(AB),9/2)
Equal(LengthOfLine(BC),3)
Equal(LengthOfLine(EF),2)
ParallelBetweenLine(AD,EB)
ParallelBetweenLine(AD,FC)
ParallelBetweenLine(EB,FC)
Goal: Value(LengthOfLine(DE))
Answer: 3
Theorem sequence:
parallel_property_alternate_interior_angle(1,AD,EB)
parallel_property_alternate_interior_angle(2,AD,EB)
parallel_property_alternate_interior_angle(1,AD,FC)
parallel_property_alternate_interior_angle(2,AD,FC)
similar_triangle_judgment_aa(1,MDA,MEB)
similar_triangle_judgment_aa(1,MDA,MFC)
similar_triangle_property_line_ratio(1,DAM,EBM)
similar_triangle_property_line_ratio(1,AMD,BME)
similar_triangle_property_line_ratio(1,DAM,FCM)
similar_triangle_property_line_ratio(1,AMD,CMF)
line_addition(1,AM,MB)
line_addition(1,AM,MC)
line_addition(1,AB,BC)
line_addition(1,DM,ME)
line_addition(1,DM,MF)
line_addition(1,DE,EF)
Problem: As shown in the diagram, Div(LengthOfLine(AO)=LengthOfLine(OD)), AB∥CD. Find the ratio of the length of line AB to the length of line CD.
问题：如图所示，Div(LengthOfLine(AO)=LengthOfLine(OD))，AB平行于CD。求直线AB的长度与直线CD的长度之比。
Construction (CDL):
Shape(AO,OB,BA)
Shape(OC,CD,DO)
Collinear(AOD)
Collinear(BOC)
Conditions (CDL):
Equal(Div(LengthOfLine(AO),LengthOfLine(OD)),2/3)
ParallelBetweenLine(AB,CD)
Goal: Value(Div(LengthOfLine(AB),LengthOfLine(CD)))
Answer: 2/3
Theorem sequence:
parallel_property_alternate_interior_angle(1,AB,CD)
parallel_property_alternate_interior_angle(2,AB,CD)
similar_triangle_judgment_aa(1,OCD,OBA)
similar_triangle_property_line_ratio(1,OCD,OBA)
similar_triangle_property_line_ratio(1,CDO,BAO)
Problem: As shown in the diagram, Div(LengthOfLine(AD)=LengthOfLine(DB)), AE=6, DE is parallel to BC. Find the length of line AC.
问题：如图所示，Div(LengthOfLine(AD)=LengthOfLine(DB))，AE=6，DE平行于BC。求直线AC的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(Div(LengthOfLine(AD),LengthOfLine(DB)),3/4)
Equal(LengthOfLine(AE),6)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(AC))
Answer: 14
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,DEA,BCA)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AD,DB)
Problem: As shown in the diagram, AB=2, BC=3, DF=4, AD∥BE, AD is parallel to CF, BE∥CF. Find the length of line DE.
问题：如图所示，AB=2，BC=3，DF=4，AD平行于BE，AD平行于CF，BE平行于CF。求直线DE的长度。
Construction (CDL):
Shape(MA,AD,DM)
Shape(AB,BE,ED,DA)
Shape(BC,CF,FE,EB)
Collinear(MABC)
Collinear(MDEF)
Conditions (CDL):
Equal(LengthOfLine(AB),2)
Equal(LengthOfLine(BC),3)
Equal(LengthOfLine(DF),4)
ParallelBetweenLine(AD,BE)
ParallelBetweenLine(AD,CF)
ParallelBetweenLine(BE,CF)
Goal: Value(LengthOfLine(DE))
Answer: 8/5
Theorem sequence:
parallel_property_corresponding_angle(1,AD,BE,M)
parallel_property_corresponding_angle(1,AD,CF,M)
parallel_property_corresponding_angle(2,EB,DA,M)
parallel_property_corresponding_angle(2,FC,DA,M)
similar_triangle_judgment_aa(1,MAD,MBE)
similar_triangle_judgment_aa(1,MAD,MCF)
similar_triangle_property_line_ratio(1,ADM,BEM)
similar_triangle_property_line_ratio(1,DMA,EMB)
similar_triangle_property_line_ratio(1,ADM,CFM)
similar_triangle_property_line_ratio(1,DMA,FMC)
line_addition(1,MA,AB)
line_addition(1,MB,BC)
line_addition(1,MD,DE)
line_addition(1,MD,DF)
Problem: As shown in the diagram, AD=3, AE=2, EC=1, DE is parallel to BC. Find the length of line AB.
问题：如图所示，AD=3，AE=2，EC=1，DE平行于BC。求直线AB的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(LengthOfLine(AD),3)
Equal(LengthOfLine(AE),2)
Equal(LengthOfLine(EC),1)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(AB))
Answer: 9/2
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,DEA,BCA)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AE,EC)
Problem: As shown in the diagram, AB=2, BC=1, BD=3, AD is parallel to EC. Find the length of line BE.
问题：如图所示，AB=2，BC=1，BD=3，AD平行于EC。求直线BE的长度。
Construction (CDL):
Shape(AB,BD,DA)
Shape(BE,EC,CB)
Collinear(EBD)
Collinear(ABC)
Conditions (CDL):
Equal(LengthOfLine(AB),2)
Equal(LengthOfLine(BC),1)
Equal(LengthOfLine(BD),3)
ParallelBetweenLine(AD,EC)
Goal: Value(LengthOfLine(BE))
Answer: 3/2
Theorem sequence:
parallel_property_alternate_interior_angle(1,AD,EC)
parallel_property_alternate_interior_angle(2,AD,EC)
similar_triangle_judgment_aa(1,BDA,BEC)
similar_triangle_property_line_ratio(1,DAB,ECB)
similar_triangle_property_line_ratio(1,ABD,CBE)
Problem: As shown in the diagram, AB=2, AC=5, DE=3/2, AD is parallel to BE, AD∥CF, BE is parallel to CF. Find the length of line DF.
问题：如图所示，AB=2，AC=5，DE=3/2，AD平行于BE，AD平行于CF，BE∥CF。求直线DF的长度。
Construction (CDL):
Shape(MA,AD,DM)
Shape(AB,BE,ED,DA)
Shape(BC,CF,FE,EB)
Collinear(MABC)
Collinear(MDEF)
Conditions (CDL):
Equal(LengthOfLine(AB),2)
Equal(LengthOfLine(AC),5)
Equal(LengthOfLine(DE),3/2)
ParallelBetweenLine(AD,BE)
ParallelBetweenLine(AD,CF)
ParallelBetweenLine(BE,CF)
Goal: Value(LengthOfLine(DF))
Answer: 15/4
Theorem sequence:
parallel_property_corresponding_angle(1,AD,BE,M)
parallel_property_corresponding_angle(1,AD,CF,M)
parallel_property_corresponding_angle(2,EB,DA,M)
parallel_property_corresponding_angle(2,FC,DA,M)
similar_triangle_judgment_aa(1,MAD,MBE)
similar_triangle_judgment_aa(1,MAD,MCF)
similar_triangle_property_line_ratio(1,ADM,BEM)
similar_triangle_property_line_ratio(1,DMA,EMB)
similar_triangle_property_line_ratio(1,ADM,CFM)
similar_triangle_property_line_ratio(1,DMA,FMC)
line_addition(1,MA,AB)
line_addition(1,MA,AC)
line_addition(1,MD,DE)
line_addition(1,MD,DF)
Problem: As shown in the diagram, AB=3, BC=2, EF=3, AD∥EB, AD is parallel to FC, EB∥FC. Find the length of line DF.
问题：如图所示，AB=3，BC=2，EF=3，AD平行于EB，AD平行于FC，EB∥FC。求直线DF的长度。
Construction (CDL):
Shape(AG,GD,DA)
Shape(GE,EB,BG)
Shape(EF,FC,CB,BE)
Collinear(AGBC)
Collinear(DGEF)
Conditions (CDL):
Equal(LengthOfLine(AB),3)
Equal(LengthOfLine(BC),2)
Equal(LengthOfLine(EF),3)
ParallelBetweenLine(AD,EB)
ParallelBetweenLine(AD,FC)
ParallelBetweenLine(EB,FC)
Goal: Value(LengthOfLine(DF))
Answer: 15/2
Theorem sequence:
parallel_property_alternate_interior_angle(1,AD,EB)
parallel_property_alternate_interior_angle(2,AD,EB)
parallel_property_alternate_interior_angle(1,AD,FC)
parallel_property_alternate_interior_angle(2,AD,FC)
similar_triangle_judgment_aa(1,GDA,GEB)
similar_triangle_judgment_aa(1,GDA,GFC)
similar_triangle_property_line_ratio(1,DAG,EBG)
similar_triangle_property_line_ratio(1,AGD,BGE)
similar_triangle_property_line_ratio(1,DAG,FCG)
similar_triangle_property_line_ratio(1,AGD,CGF)
line_addition(1,AG,GB)
line_addition(1,AG,GC)
line_addition(1,AB,BC)
line_addition(1,DG,GE)
line_addition(1,DG,GF)
line_addition(1,DE,EF)
Problem: As shown in the diagram, Div(LengthOfLine(AE)=LengthOfLine(AC)), AD=6, DE∥BC. Find the length of line AB.
问题：如图所示，Div(LengthOfLine(AE)=LengthOfLine(AC))，AD=6，DE∥BC。求直线AB的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(Div(LengthOfLine(AE),LengthOfLine(AC)),3/4)
Equal(LengthOfLine(AD),6)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(AB))
Answer: 8
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,DEA,BCA)
similar_triangle_property_line_ratio(1,EAD,CAB)
Problem: As shown in the diagram, AD=6, AE=4, DB=3, DE is parallel to BC. Find the length of line EC.
问题：如图所示，AD=6，AE=4，DB=3，DE∥BC。求直线EC的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(LengthOfLine(AD),6)
Equal(LengthOfLine(AE),4)
Equal(LengthOfLine(DB),3)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(EC))
Answer: 2
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,DEA,BCA)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AD,DB)
line_addition(1,AE,EC)
Problem: As shown in the diagram, Div(LengthOfLine(AD)=LengthOfLine(DB)), AE=6, DE∥BC. Find the length of line EC.
问题：如图所示，Div(LengthOfLine(AD)=LengthOfLine(DB))，AE=6，DE∥BC。求直线EC的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(Div(LengthOfLine(AD),LengthOfLine(DB)),2/3)
Equal(LengthOfLine(AE),6)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(EC))
Answer: 9
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,DEA,BCA)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AD,DB)
line_addition(1,AE,EC)
Problem: As shown in the diagram, Div(LengthOfLine(AD)=LengthOfLine(BD)), AE=9, DE∥BC. Find the length of line EC.
问题：如图所示，Div(LengthOfLine(AD)=LengthOfLine(BD))，AE=9，DE∥BC。求直线EC的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(Div(LengthOfLine(AD),LengthOfLine(BD)),3/4)
Equal(LengthOfLine(AE),9)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(EC))
Answer: 12
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,DEA,BCA)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AD,DB)
line_addition(1,AE,EC)
Problem: As shown in the diagram, Div(LengthOfLine(AD)=LengthOfLine(AB)), AE=5, DE∥BC. Find the length of line EC.
问题：如图所示，Div(LengthOfLine(AD)=LengthOfLine(AB))，AE=5，DE∥BC。求直线EC的长度。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(Div(LengthOfLine(AD),LengthOfLine(AB)),1/3)
Equal(LengthOfLine(AE),5)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(EC))
Answer: 10
Theorem sequence:
parallel_property_corresponding_angle(1,DE,BC,A)
parallel_property_corresponding_angle(2,CB,ED,A)
similar_triangle_judgment_aa(1,ADE,ABC)
similar_triangle_property_line_ratio(1,DEA,BCA)
similar_triangle_property_line_ratio(1,EAD,CAB)
line_addition(1,AE,EC)
Problem: As shown in the diagram, AB=2, AC=6, DE=3/2, AD is parallel to BE, AD is parallel to CF, BE is parallel to CF. Find the length of line DF.
问题：如图所示，AB=2，AC=6，DE=3/2，AD∥BE，AD∥CF，BE平行于CF。求直线DF的长度。
Construction (CDL):
Shape(MA,AD,DM)
Shape(AB,BE,ED,DA)
Shape(BC,CF,FE,EB)
Collinear(MABC)
Collinear(MDEF)
Conditions (CDL):
Equal(LengthOfLine(AB),2)
Equal(LengthOfLine(AC),6)
Equal(LengthOfLine(DE),3/2)
ParallelBetweenLine(AD,BE)
ParallelBetweenLine(AD,CF)
ParallelBetweenLine(BE,CF)
Goal: Value(LengthOfLine(DF))
Answer: 9/2
Theorem sequence:
parallel_property_corresponding_angle(1,AD,BE,M)
parallel_property_corresponding_angle(1,AD,CF,M)
parallel_property_corresponding_angle(2,EB,DA,M)
parallel_property_corresponding_angle(2,FC,DA,M)
similar_triangle_judgment_aa(1,MAD,MBE)
similar_triangle_judgment_aa(1,MAD,MCF)
similar_triangle_property_line_ratio(1,ADM,BEM)
similar_triangle_property_line_ratio(1,DMA,EMB)
similar_triangle_property_line_ratio(1,ADM,CFM)
similar_triangle_property_line_ratio(1,DMA,FMC)
line_addition(1,MA,AB)
line_addition(1,MA,AC)
line_addition(1,MD,DE)
line_addition(1,MD,DF)
Problem: As shown in the diagram, AE=BC, CE=5, CF=4, AB is parallel to DC, AB∥EF, BA is parallel to FE. Find the ratio of the length of line CE to the length of line AE.
问题：如图所示，AE=BC，CE=5，CF=4，AB平行于DC，AB∥EF，BA平行于FE。求直线CE的长度与直线AE的长度之比。
Construction (CDL):
Shape(CD,DE,EC)
Shape(CE,EF,FC)
Shape(EA,AB,BE)
Shape(FE,EB,BF)
Collinear(DEB)
Collinear(CEA)
Collinear(CFB)
Conditions (CDL):
Equal(LengthOfLine(AE),LengthOfLine(BC))
Equal(LengthOfLine(CE),5)
Equal(LengthOfLine(CF),4)
ParallelBetweenLine(AB,DC)
ParallelBetweenLine(AB,EF)
ParallelBetweenLine(BA,FE)
Goal: Value(Div(LengthOfLine(CE),LengthOfLine(AE)))
Answer: 1/4
Theorem sequence:
parallel_property_corresponding_angle(1,EF,AB,C)
parallel_property_corresponding_angle(2,BA,FE,C)
similar_triangle_judgment_aa(1,CEF,CAB)
line_addition(1,CE,EA)
similar_triangle_property_line_ratio(1,EFC,ABC)
similar_triangle_property_line_ratio(1,FCE,BCA)