SunnyLin/FormalGeo7k_v1 huggingface dataset:
Problem: As shown in the diagram, AB=6, AC=4, AD=2, ∠ADE=∠BCA. Find the length of line AE.
问题：如图所示，AB=6，AC=4，AD=2，∠ADE=∠BCA。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(LengthOfLine(AB),6)
Equal(LengthOfLine(AC),4)
Equal(LengthOfLine(AD),2)
Equal(MeasureOfAngle(ADE),MeasureOfAngle(BCA))
Goal: Value(LengthOfLine(AE))
Answer: 3
Theorem sequence:
mirror_similar_triangle_judgment_aa(1,EAD,BCA)
mirror_similar_triangle_property_line_ratio(1,EAD,BCA)
mirror_similar_triangle_property_line_ratio(1,DEA,CAB)
Problem: As shown in the diagram, Div(LengthOfLine(DB)=LengthOfLine(AD)), AE=2, DE is parallel to BC. Find the length of line AC.
问题：如图所示，Div(LengthOfLine(DB)=LengthOfLine(AD))，AE=2，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(DB),LengthOfLine(AD)),3)
Equal(LengthOfLine(AE),2)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(AC))
Answer: 8
Theorem sequence:
line_addition(1,AD,DB)
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, Div(LengthOfLine(AD)=LengthOfLine(DB)), AE=12, DE is parallel to BC. Find the length of line EC.
问题：如图所示，Div(LengthOfLine(AD)=LengthOfLine(DB))，AE=12，DE平行于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)),3/4)
Equal(LengthOfLine(AE),12)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(EC))
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)
line_addition(1,AD,DB)
line_addition(1,AE,EC)
similar_triangle_property_line_ratio(1,DEA,BCA)
similar_triangle_property_line_ratio(1,EAD,CAB)
Problem: As shown in the diagram, Div(LengthOfLine(AD)=LengthOfLine(DB)), AE=6, DE∥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)
line_addition(1,AD,DB)
similar_triangle_property_line_ratio(1,DEA,BCA)
similar_triangle_property_line_ratio(1,EAD,CAB)
Problem: As shown in the diagram, AD=4, BC=3, DF=3, AB∥CD, AB is parallel to EF, CD is parallel to EF. Find the length of line BE.
问题：如图所示，AD=4，BC=3，DF=3，AB平行于CD，AB∥EF，CD平行于EF。求直线BE的长度。
Construction (CDL):
Shape(AM,MB,BA)
Shape(MC,CD,DM)
Shape(CE,EF,FD,DC)
Collinear(AMDF)
Collinear(BMCE)
Conditions (CDL):
Equal(LengthOfLine(AD),4)
Equal(LengthOfLine(BC),3)
Equal(LengthOfLine(DF),3)
ParallelBetweenLine(AB,CD)
ParallelBetweenLine(AB,EF)
ParallelBetweenLine(CD,EF)
Goal: Value(LengthOfLine(BE))
Answer: 21/4
Theorem sequence:
parallel_property_alternate_interior_angle(1,AB,CD)
parallel_property_alternate_interior_angle(2,AB,CD)
parallel_property_alternate_interior_angle(1,AB,EF)
parallel_property_alternate_interior_angle(2,AB,EF)
similar_triangle_judgment_aa(1,MBA,MCD)
similar_triangle_judgment_aa(1,MBA,MEF)
similar_triangle_property_line_ratio(1,BAM,CDM)
similar_triangle_property_line_ratio(1,AMB,DMC)
similar_triangle_property_line_ratio(1,BAM,EFM)
similar_triangle_property_line_ratio(1,AMB,FME)
line_addition(1,AM,MD)
line_addition(1,AM,MF)
line_addition(1,AD,DF)
line_addition(1,BM,MC)
line_addition(1,BM,ME)
Problem: As shown in the diagram, AB=3, DE=2, EF=4, MD=4, DA∥EB, DA∥FC, EB is parallel to FC. Find the length of line AC.
问题：如图所示，AB=3，DE=2，EF=4，MD=4，DA∥EB，DA平行于FC，EB∥FC。求直线AC的长度。
Construction (CDL):
Shape(MD,DA,AM)
Shape(DE,EB,BA,AD)
Shape(EF,FC,CB,BE)
Collinear(MDEF)
Collinear(MABC)
Conditions (CDL):
Equal(LengthOfLine(AB),3)
Equal(LengthOfLine(DE),2)
Equal(LengthOfLine(EF),4)
Equal(LengthOfLine(MD),4)
ParallelBetweenLine(DA,EB)
ParallelBetweenLine(DA,FC)
ParallelBetweenLine(EB,FC)
Goal: Value(LengthOfLine(AC))
Answer: 9
Theorem sequence:
line_addition(1,MD,DE)
line_addition(1,ME,EF)
line_addition(1,MA,AB)
line_addition(1,MA,AC)
parallel_property_corresponding_angle(1,DA,EB,M)
parallel_property_corresponding_angle(1,DA,FC,M)
parallel_property_corresponding_angle(2,BE,AD,M)
parallel_property_corresponding_angle(2,CF,AD,M)
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)
Problem: As shown in the diagram, AB=4, AC=3, AD=3, DE∥BC. Find the length of line AE.
问题：如图所示，AB=4，AC=3，AD=3，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(LengthOfLine(AB),4)
Equal(LengthOfLine(AC),3)
Equal(LengthOfLine(AD),3)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(AE))
Answer: 9/4
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)
Problem: As shown in the diagram, AB=6, BC=4, DF=9, MB=2, AD is parallel to EB, AD is parallel to FC, EB is parallel to FC. Find the length of line DE.
问题：如图所示，AB=6，BC=4，DF=9，MB=2，AD平行于EB，AD平行于FC，EB∥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),6)
Equal(LengthOfLine(BC),4)
Equal(LengthOfLine(DF),9)
Equal(LengthOfLine(MB),2)
ParallelBetweenLine(AD,EB)
ParallelBetweenLine(AD,FC)
ParallelBetweenLine(EB,FC)
Goal: Value(LengthOfLine(DE))
Answer: 27/5
Theorem sequence:
parallel_property_alternate_interior_angle(1,AD,FC)
parallel_property_alternate_interior_angle(2,AD,FC)
parallel_property_corresponding_angle(1,EB,FC,D)
parallel_property_corresponding_angle(2,CF,BE,A)
line_addition(1,AM,MB)
line_addition(1,MB,BC)
line_addition(1,DM,ME)
line_addition(1,DM,MF)
similar_triangle_judgment_aa(1,MDA,MFC)
similar_triangle_property_line_ratio(1,DAM,FCM)
similar_triangle_property_line_ratio(1,AMD,CMF)
similar_triangle_judgment_aa(1,MEB,MFC)
similar_triangle_property_line_ratio(1,EBM,FCM)
similar_triangle_property_line_ratio(1,BME,CMF)
Problem: As shown in the diagram, AD=6, AE=4, BD=3, DE∥BC. Find the length of line EC.
问题：如图所示，AD=6，AE=4，BD=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(BD),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, AD=6, AE=4, BD=3, DE∥BC. Find the length of line AC.
问题：如图所示，AD=6，AE=4，BD=3，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),6)
Equal(LengthOfLine(AE),4)
Equal(LengthOfLine(BD),3)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(AC))
Answer: 6
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, AF=10, BE=12, CM=1, AB is parallel to CD, AB∥EF, CD∥EF. Find the length of line DE.
问题：如图所示，AC=4，AF=10，BE=12，CM=1，AB∥CD，AB平行于EF，CD平行于EF。求直线DE的长度。
Construction (CDL):
Shape(AC,CD,DB,BA)
Shape(CM,MD,DC)
Shape(ME,EF,FM)
Collinear(ACMF)
Collinear(BDME)
Conditions (CDL):
Equal(LengthOfLine(AC),4)
Equal(LengthOfLine(AF),10)
Equal(LengthOfLine(BE),12)
Equal(LengthOfLine(CM),1)
ParallelBetweenLine(AB,CD)
ParallelBetweenLine(AB,EF)
ParallelBetweenLine(CD,EF)
Goal: Value(LengthOfLine(DE))
Answer: 36/5
Theorem sequence:
parallel_property_alternate_interior_angle(1,AB,EF)
parallel_property_alternate_interior_angle(2,AB,EF)
parallel_property_alternate_interior_angle(1,CD,EF)
parallel_property_alternate_interior_angle(2,CD,EF)
line_addition(1,AC,CM)
line_addition(1,AC,CF)
line_addition(1,CM,MF)
line_addition(1,BD,DM)
line_addition(1,BD,DE)
line_addition(1,BM,ME)
similar_triangle_judgment_aa(1,MEF,MBA)
similar_triangle_property_line_ratio(1,EFM,BAM)
similar_triangle_property_line_ratio(1,FME,AMB)
similar_triangle_judgment_aa(1,MEF,MDC)
similar_triangle_property_line_ratio(1,EFM,DCM)
similar_triangle_property_line_ratio(1,FME,CMD)
Problem: As shown in the diagram, AD=Mul(LengthOfLine(BD),2), AE=2, DE∥BC. Find the length of line AC.
问题：如图所示，AD=Mul(LengthOfLine(BD),2)，AE=2，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),Mul(LengthOfLine(BD),2))
Equal(LengthOfLine(AE),2)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(AC))
Answer: 3
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, BO=5, DC=4, DO=3, DC∥AB. Find the length of line AB.
问题：如图所示，BO=5，DC=4，DO=3，DC∥AB。求直线AB的长度。
Construction (CDL):
Shape(OC,CD,DO)
Shape(OA,AB,BO)
Collinear(AOC)
Collinear(DOB)
Conditions (CDL):
Equal(LengthOfLine(BO),5)
Equal(LengthOfLine(DC),4)
Equal(LengthOfLine(DO),3)
ParallelBetweenLine(DC,AB)
Goal: Value(LengthOfLine(AB))
Answer: 20/3
Theorem sequence:
parallel_property_alternate_interior_angle(1,DC,AB)
parallel_property_alternate_interior_angle(2,DC,AB)
similar_triangle_judgment_aa(1,OAB,OCD)
similar_triangle_property_line_ratio(1,OAB,OCD)
similar_triangle_property_line_ratio(1,ABO,CDO)
Problem: As shown in the diagram, Div(LengthOfLine(AE)=LengthOfLine(EC)), AD is the angle bisector of ∠CAB, ED∥AB. Find the ratio of the length of line AC to the length of line AB.
问题：如图所示，Div(LengthOfLine(AE)=LengthOfLine(EC))，AD是∠CAB的角平分线，ED∥AB。求直线AC的长度与直线AB的长度之比。
Construction (CDL):
Shape(AB,BD,DA)
Shape(AD,DE,EA)
Shape(ED,DC,CE)
Collinear(AEC)
Collinear(BDC)
Conditions (CDL):
Equal(Div(LengthOfLine(AE),LengthOfLine(EC)),3/5)
IsBisectorOfAngle(AD,CAB)
ParallelBetweenLine(ED,AB)
Goal: Value(Div(LengthOfLine(AC),LengthOfLine(AB)))
Answer: 5/3
Theorem sequence:
parallel_property_alternate_interior_angle(2,ED,AB)
isosceles_triangle_judgment_angle_equal(1,EAD)
parallel_property_corresponding_angle(2,BA,DE,C)
similar_triangle_judgment_aa(1,EDC,ABC)
similar_triangle_property_line_ratio(1,DCE,BCA)
similar_triangle_property_line_ratio(1,CED,CAB)
line_addition(1,AE,EC)
Problem: As shown in the diagram, BD=4, BE=3, DA=2, ED∥CA. Find the length of line BC.
问题：如图所示，BD=4，BE=3，DA=2，ED∥CA。求直线BC的长度。
Construction (CDL):
Shape(DB,BE,ED)
Shape(DE,EC,CA,AD)
Collinear(BDA)
Collinear(BEC)
Conditions (CDL):
Equal(LengthOfLine(BD),4)
Equal(LengthOfLine(BE),3)
Equal(LengthOfLine(DA),2)
ParallelBetweenLine(ED,CA)
Goal: Value(LengthOfLine(BC))
Answer: 9/2
Theorem sequence:
parallel_property_corresponding_angle(1,ED,CA,B)
parallel_property_corresponding_angle(2,AC,DE,B)
similar_triangle_judgment_aa(1,BED,BCA)
similar_triangle_property_line_ratio(1,EDB,CAB)
similar_triangle_property_line_ratio(1,DBE,ABC)
line_addition(1,BD,DA)
Problem: As shown in the diagram, AE=2, CE=3, DE=4, DE is parallel to BC. Find the length of line BC.
问题：如图所示，AE=2，CE=3，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(AE),2)
Equal(LengthOfLine(CE),3)
Equal(LengthOfLine(DE),4)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(BC))
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,ADE,ABC)
similar_triangle_property_line_ratio(1,DEA,BCA)
line_addition(1,AE,EC)
Problem: As shown in the diagram, AD=1, DB=2. Find the ratio of the length of line AD to the length of line AB.
问题：如图所示，AD=1，DB=2。求直线AD的长度与直线AB的长度之比。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(LengthOfLine(AD),1)
Equal(LengthOfLine(DB),2)
Goal: Value(Div(LengthOfLine(AD),LengthOfLine(AB)))
Answer: 1/3
Theorem sequence:
line_addition(1,AD,DB)
Problem: As shown in the diagram, AB=4, AC=3, AD=3, DE is parallel to BC. Find the length of line AE.
问题：如图所示，AB=4，AC=3，AD=3，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(LengthOfLine(AB),4)
Equal(LengthOfLine(AC),3)
Equal(LengthOfLine(AD),3)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(AE))
Answer: 9/4
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)
Problem: As shown in the diagram, AB=2, AM=3, CB=3, DE=3, AD is parallel to BE, AD∥CF, BE is parallel to CF. Find the length of line EF.
问题：如图所示，AB=2，AM=3，CB=3，DE=3，AD平行于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),2)
Equal(LengthOfLine(AM),3)
Equal(LengthOfLine(CB),3)
Equal(LengthOfLine(DE),3)
ParallelBetweenLine(AD,BE)
ParallelBetweenLine(AD,CF)
ParallelBetweenLine(BE,CF)
Goal: Value(LengthOfLine(EF))
Answer: 9/2
Theorem sequence:
parallel_property_corresponding_angle(1,AD,BE,M)
parallel_property_corresponding_angle(1,BE,CF,M)
parallel_property_corresponding_angle(2,EB,DA,M)
parallel_property_corresponding_angle(2,FC,EB,M)
line_addition(1,MA,AB)
line_addition(1,MB,BC)
line_addition(1,MD,DE)
line_addition(1,ME,EF)
similar_triangle_judgment_aa(1,MAD,MBE)
similar_triangle_judgment_aa(1,MBE,MCF)
similar_triangle_property_line_ratio(1,ADM,BEM)
similar_triangle_property_line_ratio(1,DMA,EMB)
similar_triangle_property_line_ratio(1,BEM,CFM)
similar_triangle_property_line_ratio(1,EMB,FMC)
Problem: As shown in the diagram, AB=5, AM=10, CB=10, DE=4, AD∥BE, AD∥CF, BE∥CF. Find the length of line EF.
问题：如图所示，AB=5，AM=10，CB=10，DE=4，AD平行于BE，AD平行于CF，BE∥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),5)
Equal(LengthOfLine(AM),10)
Equal(LengthOfLine(CB),10)
Equal(LengthOfLine(DE),4)
ParallelBetweenLine(AD,BE)
ParallelBetweenLine(AD,CF)
ParallelBetweenLine(BE,CF)
Goal: Value(LengthOfLine(EF))
Answer: 8
Theorem sequence:
parallel_property_corresponding_angle(1,AD,BE,M)
parallel_property_corresponding_angle(1,BE,CF,M)
parallel_property_corresponding_angle(2,EB,DA,M)
parallel_property_corresponding_angle(2,FC,EB,M)
line_addition(1,MA,AB)
line_addition(1,MB,BC)
line_addition(1,MD,DE)
line_addition(1,ME,EF)
similar_triangle_judgment_aa(1,MAD,MBE)
similar_triangle_judgment_aa(1,MBE,MCF)
similar_triangle_property_line_ratio(1,ADM,BEM)
similar_triangle_property_line_ratio(1,DMA,EMB)
similar_triangle_property_line_ratio(1,BEM,CFM)
similar_triangle_property_line_ratio(1,EMB,FMC)
Problem: As shown in the diagram, AF=4, BD=CD, Mul(LengthOfLine(AE)=2), BF is parallel to DG. Find the length of line AC.
问题：如图所示，AF=4，BD=CD，Mul(LengthOfLine(AE)=2)，BF平行于DG。求直线AC的长度。
Construction (CDL):
Shape(EB,BD,DE)
Shape(ED,DG,GF,FE)
Shape(DC,CG,GD)
Shape(AE,EF,FA)
Collinear(AED)
Collinear(AFGC)
Collinear(BEF)
Collinear(BDC)
Conditions (CDL):
Equal(LengthOfLine(AF),4)
Equal(LengthOfLine(BD),LengthOfLine(CD))
Equal(Mul(LengthOfLine(AE),2),LengthOfLine(ED))
ParallelBetweenLine(BF,DG)
Goal: Value(LengthOfLine(AC))
Answer: 20
Theorem sequence:
parallel_property_collinear_extend(3,BF,DG,E)
parallel_property_corresponding_angle(1,GD,FB,C)
parallel_property_corresponding_angle(1,EF,DG,A)
parallel_property_corresponding_angle(2,GD,FB,A)
similar_triangle_judgment_aa(1,DCG,BCF)
similar_triangle_judgment_aa(1,AEF,ADG)
similar_triangle_property_line_ratio(1,DCG,BCF)
similar_triangle_property_line_ratio(1,GDC,FBC)
similar_triangle_property_line_ratio(1,EFA,DGA)
similar_triangle_property_line_ratio(1,FAE,GAD)
line_addition(1,AE,ED)
line_addition(1,AF,FC)
line_addition(1,AG,GC)
line_addition(1,BD,DC)
Problem: As shown in the diagram, AD=Mul(LengthOfLine(BD),2), AE=6, DE is parallel to BC. Find the length of line EC.
问题：如图所示，AD=Mul(LengthOfLine(BD),2)，AE=6，DE平行于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),Mul(LengthOfLine(BD),2))
Equal(LengthOfLine(AE),6)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(EC))
Answer: 3
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, AB=3, CB=4, DE=3, MA=5, 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=3，CB=4，DE=3，MA=5，AD平行于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),3)
Equal(LengthOfLine(CB),4)
Equal(LengthOfLine(DE),3)
Equal(LengthOfLine(MA),5)
ParallelBetweenLine(AD,BE)
ParallelBetweenLine(AD,CF)
ParallelBetweenLine(BE,CF)
Goal: Value(LengthOfLine(DF))
Answer: 7
Theorem sequence:
parallel_property_corresponding_angle(1,AD,BE,M)
parallel_property_corresponding_angle(1,BE,CF,M)
parallel_property_corresponding_angle(2,EB,DA,M)
parallel_property_corresponding_angle(2,FC,EB,M)
line_addition(1,MA,AB)
line_addition(1,MB,BC)
line_addition(1,MD,DE)
line_addition(1,MD,DF)
similar_triangle_judgment_aa(1,MAD,MBE)
similar_triangle_judgment_aa(1,MBE,MCF)
similar_triangle_property_line_ratio(1,ADM,BEM)
similar_triangle_property_line_ratio(1,DMA,EMB)
similar_triangle_property_line_ratio(1,BEM,CFM)
similar_triangle_property_line_ratio(1,EMB,FMC)
Problem: As shown in the diagram, Div(LengthOfLine(AD)=LengthOfLine(BD)), EC=8, DE∥BC. Find the length of line AE.
问题：如图所示，Div(LengthOfLine(AD)=LengthOfLine(BD))，EC=8，DE∥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(BD)),3/4)
Equal(LengthOfLine(EC),8)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(AE))
Answer: 6
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, AC=4, AE=10, BF=15/2, MA=6, AB∥CD, AB is parallel to EF, CD is parallel to EF. Find the length of line DF.
问题：如图所示，AC=4，AE=10，BF=15/2，MA=6，AB∥CD，AB∥EF，CD平行于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),4)
Equal(LengthOfLine(AE),10)
Equal(LengthOfLine(BF),15/2)
Equal(LengthOfLine(MA),6)
ParallelBetweenLine(AB,CD)
ParallelBetweenLine(AB,EF)
ParallelBetweenLine(CD,EF)
Goal: Value(LengthOfLine(DF))
Answer: 9/2
Theorem sequence:
parallel_property_corresponding_angle(1,AB,CD,M)
parallel_property_corresponding_angle(1,CD,EF,M)
parallel_property_corresponding_angle(2,DC,BA,M)
parallel_property_corresponding_angle(2,FE,DC,M)
line_addition(1,MA,AC)
line_addition(1,MA,AE)
line_addition(1,MB,BF)
line_addition(1,MD,DF)
similar_triangle_judgment_aa(1,MAB,MCD)
similar_triangle_judgment_aa(1,MCD,MEF)
similar_triangle_property_line_ratio(1,ABM,CDM)
similar_triangle_property_line_ratio(1,BMA,DMC)
similar_triangle_property_line_ratio(1,CDM,EFM)
similar_triangle_property_line_ratio(1,DMC,FME)
Problem: As shown in the diagram, AB=2, AC=6, EF=5, 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，EF=5，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),6)
Equal(LengthOfLine(EF),5)
ParallelBetweenLine(AD,BE)
ParallelBetweenLine(AD,CF)
ParallelBetweenLine(BE,CF)
Goal: Value(LengthOfLine(DF))
Answer: 15/2
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,DF)
line_addition(1,ME,EF)
Problem: As shown in the diagram, AD=6, AE=Mul(LengthOfLine(EC),3), DE∥BC. Find the length of line BD.
问题：如图所示，AD=6，AE=Mul(LengthOfLine(EC),3)，DE平行于BC。求直线BD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),Mul(LengthOfLine(EC),3))
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(BD))
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, AD=3, AE=2, BD=2, DE∥BC. Find the length of line EC.
问题：如图所示，AD=3，AE=2，BD=2，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),3)
Equal(LengthOfLine(AE),2)
Equal(LengthOfLine(BD),2)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(EC))
Answer: 4/3
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, AD=2, AE=1, DB=4, DE∥BC. Find the length of line AC.
问题：如图所示，AD=2，AE=1，DB=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(LengthOfLine(AD),2)
Equal(LengthOfLine(AE),1)
Equal(LengthOfLine(DB),4)
ParallelBetweenLine(DE,BC)
Goal: Value(LengthOfLine(AC))
Answer: 3
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)