SunnyLin/FormalGeo7k_v1 huggingface dataset:
Problem: As shown in the diagram, AB=AC, ∠ABC=25°, AD is the median of triangle ABC. Find the measure of ∠DAB.
问题：如图所示，AB=AC，∠ABC=25°，AD是△ABC的中线。求∠DAB的大小。
Construction (CDL):
Shape(AB,BD,DA)
Shape(AD,DC,CA)
Collinear(BDC)
Conditions (CDL):
Equal(LengthOfLine(AB),LengthOfLine(AC))
Equal(MeasureOfAngle(ABC),25)
IsMedianOfTriangle(AD,ABC)
Goal: Value(MeasureOfAngle(DAB))
Answer: 65
Theorem sequence:
isosceles_triangle_judgment_line_equal(1,ABC)
isosceles_triangle_property_angle_equal(1,ABC)
triangle_property_angle_sum(1,ABD)
mirror_congruent_triangle_judgment_sas(1,BDA,CAD)
mirror_congruent_triangle_property_angle_equal(1,DAB,DCA)
adjacent_complementary_angle(1,BDA,ADC)
Problem: As shown in the diagram, OC=OE, ∠BAO=50°, AB is parallel to OD. Find the measure of ∠OCE.
问题：如图所示，OC=OE，∠BAO=50°，AB平行于OD。求∠OCE的大小。
Construction (CDL):
Shape(BA,AO)
Shape(AO,OD)
Shape(DO,OE)
Shape(OC,CE,EO)
Collinear(AOE)
Collinear(COD)
Conditions (CDL):
Equal(LengthOfLine(OC),LengthOfLine(OE))
Equal(MeasureOfAngle(BAO),50)
ParallelBetweenLine(AB,OD)
Goal: Value(MeasureOfAngle(OCE))
Answer: 25
Theorem sequence:
parallel_property_corresponding_angle(2,AB,OD,E)
adjacent_complementary_angle(1,DOE,EOC)
triangle_property_angle_sum(1,OCE)
isosceles_triangle_judgment_line_equal(1,OCE)
isosceles_triangle_property_angle_equal(1,OCE)
Problem: As shown in the diagram, ∠DEA=40°, triangle ABC is an equilateral triangle, DE∥PC, PC is parallel to BF. Find the measure of ∠CBF.
问题：如图所示，∠DEA=40°，三角形ABC为等边三角形，DE∥PC，PC∥BF。求∠CBF的大小。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DP,PC,CE,ED)
Shape(PB,BC,CP)
Shape(CB,BF)
Collinear(ADPB)
Collinear(AEC)
Conditions (CDL):
Equal(MeasureOfAngle(DEA),40)
EquilateralTriangle(ABC)
ParallelBetweenLine(DE,PC)
ParallelBetweenLine(PC,BF)
Goal: Value(MeasureOfAngle(CBF))
Answer: 20
Theorem sequence:
equilateral_triangle_property_angle(1,CAB)
parallel_property_corresponding_angle(2,CP,ED,A)
angle_addition(1,BCP,PCA)
parallel_property_alternate_interior_angle(2,PC,BF)
Problem: As shown in the diagram, AD=AO, triangle ABC is an equilateral triangle, BO is the median of △ BCA. Find the measure of ∠BOD.
问题：如图所示，AD=AO，三角形ABC为等边三角形，BO是三角形BCA的中线。求∠BOD的大小。
Construction (CDL):
Shape(OD,DA,AO)
Shape(CO,OB,BC)
Shape(OA,AB,BO)
Collinear(DAB)
Collinear(COA)
Conditions (CDL):
Equal(LengthOfLine(AD),LengthOfLine(AO))
EquilateralTriangle(ABC)
IsMedianOfTriangle(BO,BCA)
Goal: Value(MeasureOfAngle(BOD))
Answer: 120
Theorem sequence:
equilateral_triangle_property_angle(1,ABC)
adjacent_complementary_angle(1,DAO,OAB)
isosceles_triangle_judgment_line_equal(1,AOD)
isosceles_triangle_property_angle_equal(1,AOD)
triangle_property_angle_sum(1,ODA)
triangle_property_angle_sum(1,OAB)
triangle_property_angle_sum(1,ODB)
isosceles_triangle_property_line_coincidence(2,BCA,O)
Problem: As shown in the diagram, AC=BC, ∠ECD=70°, CD∥AB. Find the measure of ∠BCA.
问题：如图所示，AC=BC，∠ECD=70°，CD平行于AB。求∠BCA的大小。
Construction (CDL):
Shape(EC,CD)
Shape(DC,CB)
Shape(CA,AB,BC)
Collinear(ECA)
Conditions (CDL):
Equal(LengthOfLine(AC),LengthOfLine(BC))
Equal(MeasureOfAngle(ECD),70)
ParallelBetweenLine(CD,AB)
Goal: Value(MeasureOfAngle(BCA))
Answer: 40
Theorem sequence:
isosceles_triangle_judgment_line_equal(1,CAB)
isosceles_triangle_property_angle_equal(1,CAB)
triangle_property_angle_sum(1,CAB)
parallel_property_corresponding_angle(1,CD,AB,E)
Problem: As shown in the diagram, AD=BC, ∠EPF=130°, E is the midpoint of segment AB, F is the midpoint of segment CD, P bisects segment DB. Find the measure of ∠FEP.
问题：如图所示，AD=BC，∠EPF=130°，E平分线段AB，F平分线段CD，P是线段DB的中点。求∠FEP的大小。
Construction (CDL):
Shape(DA,AE,EP,PD)
Shape(PE,EB,BP)
Shape(PF,FD,DP)
Shape(CF,FP,PB,BC)
Shape(FE,EP,PF)
Collinear(CFD)
Collinear(DPB)
Collinear(AEB)
Conditions (CDL):
Equal(LengthOfLine(AD),LengthOfLine(BC))
Equal(MeasureOfAngle(EPF),130)
IsMidpointOfLine(E,AB)
IsMidpointOfLine(F,CD)
IsMidpointOfLine(P,DB)
Goal: Value(MeasureOfAngle(FEP))
Answer: 25
Theorem sequence:
midsegment_of_triangle_judgment_midpoint(1,PE,BDA)
midsegment_of_triangle_judgment_midpoint(1,PF,DBC)
midsegment_of_triangle_property_length(1,PE,BDA)
midsegment_of_triangle_property_length(1,PF,DBC)
isosceles_triangle_judgment_line_equal(1,PFE)
triangle_property_angle_sum(1,FEP)
isosceles_triangle_property_angle_equal(1,PFE)
Problem: As shown in the diagram, ∠ABC=50°, ∠CAB=60°, D bisects segment AB, E is the midpoint of segment AC. Find the measure of ∠DEA.
问题：如图所示，∠ABC=50°，∠CAB=60°，D是线段AB的中点，E是线段AC的中点。求∠DEA的大小。
Construction (CDL):
Shape(AD,DE,EA)
Shape(DB,BC,CE,ED)
Collinear(ADB)
Collinear(AEC)
Conditions (CDL):
Equal(MeasureOfAngle(ABC),50)
Equal(MeasureOfAngle(CAB),60)
IsMidpointOfLine(D,AB)
IsMidpointOfLine(E,AC)
Goal: Value(MeasureOfAngle(DEA))
Answer: 70
Theorem sequence:
triangle_property_angle_sum(1,ABC)
midsegment_of_triangle_judgment_midpoint(1,DE,ABC)
midsegment_of_triangle_property_parallel(1,DE,ABC)
parallel_property_corresponding_angle(2,CB,ED,A)
Problem: As shown in the diagram, ∠CDA=135°, ∠DAC=23°, BA and CD are opposite sides of the ▱ ABCD. Find the measure of ∠CAB.
问题：如图所示，∠CDA=135°，∠DAC=23°，四边形ABCD是平行四边形。求∠CAB的大小。
Construction (CDL):
Shape(CD,DA,AC)
Shape(CA,AB,BC)
Conditions (CDL):
Equal(MeasureOfAngle(CDA),135)
Equal(MeasureOfAngle(DAC),23)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(CAB))
Answer: 22
Theorem sequence:
parallel_property_ipsilateral_internal_angle(1,DC,AB)
angle_addition(1,DAC,CAB)
Problem: As shown in the diagram, ∠ABC=70°, BA and CD are opposite sides of the parallelogram ABCD, AE is perpendicular to DE. Find the measure of ∠DAE.
问题：如图所示，∠ABC=70°，四边形ABCD是平行四边形，AE⊥DE。求∠DAE的大小。
Construction (CDL):
Shape(AB,BC,CE,EA)
Shape(AE,ED,DA)
Collinear(CED)
Conditions (CDL):
Equal(MeasureOfAngle(ABC),70)
Parallelogram(ABCD)
PerpendicularBetweenLine(AE,DE)
Goal: Value(MeasureOfAngle(DAE))
Answer: 20
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,BCDA)
triangle_property_angle_sum(1,AED)
Problem: As shown in the diagram, ∠ABC=125°, ∠DAC=21°, ABCD is a ▱. Find the measure of ∠CAB.
问题：如图所示，∠ABC=125°，∠DAC=21°，BA和CD是平行四边形ABCD的一组对边。求∠CAB的大小。
Construction (CDL):
Shape(AB,BC,CA)
Shape(AC,CD,DA)
Conditions (CDL):
Equal(MeasureOfAngle(ABC),125)
Equal(MeasureOfAngle(DAC),21)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(CAB))
Answer: 34
Theorem sequence:
parallel_property_ipsilateral_internal_angle(1,AD,BC)
angle_addition(1,DAC,CAB)
Problem: As shown in the diagram, AB=AC, ∠BAC=40°, BEDC is a ▱. Find the measure of ∠BED.
问题：如图所示，AB=AC，∠BAC=40°，EB和DC是▱BEDC的一组对边。求∠BED的大小。
Construction (CDL):
Shape(AD,DC,CB,BA)
Shape(BE,ED,DC,CB)
Collinear(ADC)
Conditions (CDL):
Equal(LengthOfLine(AB),LengthOfLine(AC))
Equal(MeasureOfAngle(BAC),40)
Parallelogram(BEDC)
Goal: Value(MeasureOfAngle(BED))
Answer: 70
Theorem sequence:
isosceles_triangle_judgment_line_equal(1,ACB)
isosceles_triangle_property_angle_equal(1,ACB)
triangle_property_angle_sum(1,ACB)
parallelogram_property_opposite_angle_equal(1,EDCB)
Problem: As shown in the diagram, ∠DAB=60°, BA and CD are opposite sides of the ▱ ABCD. Find the measure of ∠BCD.
问题：如图所示，∠DAB=60°，ABCD是平行四边形。求∠BCD的大小。
Construction (CDL):
Shape(AB,BC,CD,DA)
Conditions (CDL):
Equal(MeasureOfAngle(DAB),60)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(BCD))
Answer: 60
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,ABCD)
Problem: As shown in the diagram, AE=BE, BC=BE, ∠CDA=105°, quadrilateral ABCD is a ▱. Find the measure of ∠CAB.
问题：如图所示，AE=BE，BC=BE，∠CDA=105°，四边形ABCD是▱。求∠CAB的大小。
Construction (CDL):
Shape(AB,BE,EA)
Shape(CE,EB,BC)
Shape(DA,AE,EC,CD)
Collinear(AEC)
Conditions (CDL):
Equal(LengthOfLine(AE),LengthOfLine(BE))
Equal(LengthOfLine(BC),LengthOfLine(BE))
Equal(MeasureOfAngle(CDA),105)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(CAB))
Answer: 25
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,BCDA)
angle_addition(1,ABE,EBC)
isosceles_triangle_judgment_line_equal(1,EAB)
isosceles_triangle_judgment_line_equal(1,BCE)
isosceles_triangle_property_angle_equal(1,EAB)
isosceles_triangle_property_angle_equal(1,BCE)
triangle_property_angle_sum(1,CEB)
triangle_property_angle_sum(1,ABC)
Problem: As shown in the diagram, ∠AED=30°, ∠CAB=35°, D bisects segment AC, E is the midpoint of segment AB. Find the measure of ∠ACF.
问题：如图所示，∠AED=30°，∠CAB=35°，D平分线段AC，E平分线段AB。求∠ACF的大小。
Construction (CDL):
Shape(AE,ED,DA)
Shape(EB,BC,CD,DE)
Shape(AC,CF)
Collinear(AEB)
Collinear(ADC)
Collinear(BCF)
Conditions (CDL):
Equal(MeasureOfAngle(AED),30)
Equal(MeasureOfAngle(CAB),35)
IsMidpointOfLine(D,AC)
IsMidpointOfLine(E,AB)
Goal: Value(MeasureOfAngle(ACF))
Answer: 65
Theorem sequence:
midsegment_of_triangle_judgment_midpoint(1,ED,ABC)
midsegment_of_triangle_property_parallel(1,ED,ABC)
parallel_property_corresponding_angle(1,ED,BC,A)
triangle_property_angle_sum(1,ABC)
adjacent_complementary_angle(1,BCD,DCF)
Problem: As shown in the diagram, ∠DAB=60°, BE bisects ∠ABC, AD and BC are opposite sides of the ▱ ABCD. Find the measure of ∠BED.
问题：如图所示，∠DAB=60°，BE是∠ABC的角平分线，四边形ABCD是▱。求∠BED的大小。
Construction (CDL):
Shape(AB,BE,ED,DA)
Shape(CE,EB,BC)
Collinear(DEC)
Conditions (CDL):
Equal(MeasureOfAngle(DAB),60)
IsBisectorOfAngle(BE,ABC)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(BED))
Answer: 120
Theorem sequence:
parallel_property_ipsilateral_internal_angle(1,AD,BC)
parallel_property_ipsilateral_internal_angle(1,BA,CD)
angle_addition(1,ABE,EBC)
adjacent_complementary_angle(1,CEB,BED)
triangle_property_angle_sum(1,CEB)
Problem: As shown in the diagram, BD=BC, ∠BCD=55°, quadrilateral ABCD is a parallelogram, BE is perpendicular to AE. Find the measure of ∠EAB.
问题：如图所示，BD=BC，∠BCD=55°，AD和BC是平行四边形ABCD的一组对边，BE⊥AE。求∠EAB的大小。
Construction (CDL):
Shape(DA,AE,ED)
Shape(EA,AB,BE)
Shape(CD,DE,EB,BC)
Collinear(DEB)
Conditions (CDL):
Equal(LengthOfLine(BD),LengthOfLine(BC))
Equal(MeasureOfAngle(BCD),55)
Parallelogram(ABCD)
PerpendicularBetweenLine(BE,AE)
Goal: Value(MeasureOfAngle(EAB))
Answer: 35
Theorem sequence:
isosceles_triangle_judgment_line_equal(1,BCD)
isosceles_triangle_property_angle_equal(1,BCD)
triangle_property_angle_sum(1,EAB)
triangle_property_angle_sum(1,CDB)
angle_addition(1,ABE,EBC)
parallel_property_ipsilateral_internal_angle(1,BA,CD)
Problem: As shown in the diagram, Add(MeasureOfAngle(BAD)=MeasureOfAngle(DCB)), AB and DC are opposite sides of the parallelogram BADC. Find the measure of ∠CBA.
问题：如图所示，Add(MeasureOfAngle(BAD)=MeasureOfAngle(DCB))，BC和AD是平行四边形BADC的一组对边。求∠CBA的大小。
Construction (CDL):
Shape(BA,AD,DC,CB)
Conditions (CDL):
Equal(Add(MeasureOfAngle(BAD),MeasureOfAngle(DCB)),130)
Parallelogram(BADC)
Goal: Value(MeasureOfAngle(CBA))
Answer: 115
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,BADC)
quadrilateral_property_angle_sum(1,BADC)
Problem: As shown in the diagram, ∠ABC=70°, AD and BC are opposite sides of the parallelogram ABCD. Find the measure of ∠CDA.
问题：如图所示，∠ABC=70°，AD和BC是平行四边形ABCD的一组对边。求∠CDA的大小。
Construction (CDL):
Shape(AB,BC,CD,DA)
Conditions (CDL):
Equal(MeasureOfAngle(ABC),70)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(CDA))
Answer: 70
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,BCDA)
Problem: As shown in the diagram, Add(MeasureOfAngle(DAB)=MeasureOfAngle(BCD)), quadrilateral DABC is a ▱. Find the measure of ∠ABC.
问题：如图所示，Add(MeasureOfAngle(DAB)=MeasureOfAngle(BCD))，四边形DABC是平行四边形。求∠ABC的大小。
Construction (CDL):
Shape(DA,AB,BC,CD)
Conditions (CDL):
Equal(Add(MeasureOfAngle(DAB),MeasureOfAngle(BCD)),160)
Parallelogram(DABC)
Goal: Value(MeasureOfAngle(ABC))
Answer: 100
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,DABC)
quadrilateral_property_angle_sum(1,DABC)
Problem: As shown in the diagram, Add(MeasureOfAngle(ABC)=MeasureOfAngle(CDA)), BA and CD are opposite sides of the ▱ ABCD. Find the measure of ∠DAB.
问题：如图所示，Add(MeasureOfAngle(ABC)=MeasureOfAngle(CDA))，AD和BC是▱ABCD的一组对边。求∠DAB的大小。
Construction (CDL):
Shape(AB,BC,CD,DA)
Conditions (CDL):
Equal(Add(MeasureOfAngle(ABC),MeasureOfAngle(CDA)),100)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(DAB))
Answer: 130
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,ABCD)
quadrilateral_property_angle_sum(1,ABCD)
Problem: As shown in the diagram, Add(MeasureOfAngle(ABC)=MeasureOfAngle(CDA)), BA and CD are opposite sides of the parallelogram ABCD. Find the measure of ∠BCD.
问题：如图所示，Add(MeasureOfAngle(ABC)=MeasureOfAngle(CDA))，四边形ABCD是▱。求∠BCD的大小。
Construction (CDL):
Shape(AB,BC,CD,DA)
Conditions (CDL):
Equal(Add(MeasureOfAngle(ABC),MeasureOfAngle(CDA)),140)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(BCD))
Answer: 110
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,ABCD)
quadrilateral_property_angle_sum(1,ABCD)
Problem: As shown in the diagram, ∠DAB=115°, ∠DBC=25°, ABCD is a ▱. Find the measure of ∠CDB.
问题：如图所示，∠DAB=115°，∠DBC=25°，ABCD是▱。求∠CDB的大小。
Construction (CDL):
Shape(AB,BD,DA)
Shape(DB,BC,CD)
Conditions (CDL):
Equal(MeasureOfAngle(DAB),115)
Equal(MeasureOfAngle(DBC),25)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(CDB))
Answer: 40
Theorem sequence:
triangle_property_angle_sum(1,DBC)
parallelogram_property_opposite_angle_equal(1,ABCD)
Problem: As shown in the diagram, ∠DAB=150°, quadrilateral ABCD is a ▱. Find the measure of ∠BCD.
问题：如图所示，∠DAB=150°，ABCD是▱。求∠BCD的大小。
Construction (CDL):
Shape(AB,BC,CD,DA)
Conditions (CDL):
Equal(MeasureOfAngle(DAB),150)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(BCD))
Answer: 150
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,ABCD)
Problem: As shown in the diagram, Add(MeasureOfAngle(ABC)=MeasureOfAngle(CDA)), BA and CD are opposite sides of the parallelogram ABCD. Find the measure of ∠DAB.
问题：如图所示，Add(MeasureOfAngle(ABC)=MeasureOfAngle(CDA))，BA和CD是平行四边形ABCD的一组对边。求∠DAB的大小。
Construction (CDL):
Shape(AB,BC,CD,DA)
Conditions (CDL):
Equal(Add(MeasureOfAngle(ABC),MeasureOfAngle(CDA)),200)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(DAB))
Answer: 80
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,ABCD)
quadrilateral_property_angle_sum(1,ABCD)
Problem: As shown in the diagram, AB=BD, CE=CB, ∠BDA=65°, ABCD is a ▱. Find the measure of ∠ECD.
问题：如图所示，AB=BD，CE=CB，∠BDA=65°，BA和CD是平行四边形ABCD的一组对边。求∠ECD的大小。
Construction (CDL):
Shape(AB,BE,ED,DA)
Shape(DE,EC,CD)
Shape(CE,EB,BC)
Collinear(DEB)
Conditions (CDL):
Equal(LengthOfLine(AB),LengthOfLine(BD))
Equal(LengthOfLine(CE),LengthOfLine(CB))
Equal(MeasureOfAngle(BDA),65)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(ECD))
Answer: 15
Theorem sequence:
parallel_property_alternate_interior_angle(2,AD,BC)
isosceles_triangle_judgment_line_equal(1,BDA)
isosceles_triangle_judgment_line_equal(1,CEB)
isosceles_triangle_property_angle_equal(1,BDA)
isosceles_triangle_property_angle_equal(1,CEB)
angle_addition(1,BCE,ECD)
parallel_property_ipsilateral_internal_angle(1,AD,BC)
parallel_property_ipsilateral_internal_angle(1,BA,CD)
triangle_property_angle_sum(1,CEB)
Problem: As shown in the diagram, ∠CDA=120°, BA and CD are opposite sides of the ▱ ABCD. Find the measure of ∠CBM.
问题：如图所示，∠CDA=120°，BA和CD是平行四边形ABCD的一组对边。求∠CBM的大小。
Construction (CDL):
Shape(AB,BC,CD,DA)
Shape(CB,BM)
Collinear(ABM)
Conditions (CDL):
Equal(MeasureOfAngle(CDA),120)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(CBM))
Answer: 60
Theorem sequence:
adjacent_complementary_angle(1,ABC,CBM)
parallelogram_property_opposite_angle_equal(1,BCDA)
Problem: As shown in the diagram, Add(MeasureOfAngle(DAB)=MeasureOfAngle(BCD)), ABCD is a parallelogram. Find the measure of ∠ABC.
问题：如图所示，Add(MeasureOfAngle(DAB)=MeasureOfAngle(BCD))，BA和CD是▱ABCD的一组对边。求∠ABC的大小。
Construction (CDL):
Shape(AB,BC,CD,DA)
Conditions (CDL):
Equal(Add(MeasureOfAngle(DAB),MeasureOfAngle(BCD)),110)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(ABC))
Answer: 125
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,BCDA)
quadrilateral_property_angle_sum(1,ABCD)
Problem: As shown in the diagram, AE=DE, ∠DEA=46°, AB and DC are opposite sides of the parallelogram ADCB. Find the measure of ∠CBA.
问题：如图所示，AE=DE，∠DEA=46°，ADCB是▱。求∠CBA的大小。
Construction (CDL):
Shape(AD,DC,CB,BA)
Shape(AD,DC,CE,EA)
Collinear(DCE)
Conditions (CDL):
Equal(LengthOfLine(AE),LengthOfLine(DE))
Equal(MeasureOfAngle(DEA),46)
Parallelogram(ADCB)
Goal: Value(MeasureOfAngle(CBA))
Answer: 67
Theorem sequence:
triangle_property_angle_sum(1,ADE)
isosceles_triangle_judgment_line_equal(1,EAD)
isosceles_triangle_property_angle_equal(1,EAD)
parallelogram_property_opposite_angle_equal(1,DCBA)
Problem: As shown in the diagram, Mul(MeasureOfAngle(DAB)=1), BA and CD are opposite sides of the ▱ ABCD. Find the measure of ∠CDA.
问题：如图所示，Mul(MeasureOfAngle(DAB)=1)，四边形ABCD是平行四边形。求∠CDA的大小。
Construction (CDL):
Shape(AB,BC,CD,DA)
Conditions (CDL):
Equal(Mul(MeasureOfAngle(DAB),1),Mul(MeasureOfAngle(ABC),2))
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(CDA))
Answer: 60
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,ABCD)
parallelogram_property_opposite_angle_equal(1,BCDA)
quadrilateral_property_angle_sum(1,ABCD)
Problem: As shown in the diagram, Add(MeasureOfAngle(BAD)=MeasureOfAngle(DCB)), AB and DC are opposite sides of the parallelogram BADC. Find the measure of ∠ADC.
问题：如图所示，Add(MeasureOfAngle(BAD)=MeasureOfAngle(DCB))，BADC是▱。求∠ADC的大小。
Construction (CDL):
Shape(BA,AD,DC,CB)
Conditions (CDL):
Equal(Add(MeasureOfAngle(BAD),MeasureOfAngle(DCB)),120)
Parallelogram(BADC)
Goal: Value(MeasureOfAngle(ADC))
Answer: 120
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,BADC)
quadrilateral_property_angle_sum(1,BADC)
Problem: As shown in the diagram, ∠DAB=110°, BA and CD are opposite sides of the parallelogram ABCD. Find the measure of ∠DCE.
问题：如图所示，∠DAB=110°，BA和CD是▱ABCD的一组对边。求∠DCE的大小。
Construction (CDL):
Shape(AB,BC,CD,DA)
Shape(DC,CE)
Collinear(BCE)
Conditions (CDL):
Equal(MeasureOfAngle(DAB),110)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(DCE))
Answer: 70
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,ABCD)
adjacent_complementary_angle(1,BCD,DCE)
Problem: As shown in the diagram, ∠CDA=58°, AE bisects ∠DAB, quadrilateral ABCD is a parallelogram. Find the measure of ∠AEC.
问题：如图所示，∠CDA=58°，AE是∠DAB的角平分线，AD和BC是▱ABCD的一组对边。求∠AEC的大小。
Construction (CDL):
Shape(AB,BE,EA)
Shape(AE,EC,CD,DA)
Collinear(BEC)
Conditions (CDL):
Equal(MeasureOfAngle(CDA),58)
IsBisectorOfAngle(AE,DAB)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(AEC))
Answer: 119
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,BCDA)
parallel_property_ipsilateral_internal_angle(1,DC,AB)
triangle_property_angle_sum(1,ABE)
angle_addition(1,DAE,EAB)
adjacent_complementary_angle(1,BEA,AEC)
Problem: As shown in the diagram, AB=AC, ∠BAC=40°, quadrilateral EDCB is a ▱. Find the measure of ∠BED.
问题：如图所示，AB=AC，∠BAC=40°，EDCB是平行四边形。求∠BED的大小。
Construction (CDL):
Shape(BA,AD,DC,CB)
Shape(BE,ED,DC,CB)
Collinear(ADC)
Conditions (CDL):
Equal(LengthOfLine(AB),LengthOfLine(AC))
Equal(MeasureOfAngle(BAC),40)
Parallelogram(EDCB)
Goal: Value(MeasureOfAngle(BED))
Answer: 70
Theorem sequence:
isosceles_triangle_judgment_line_equal(1,ACB)
isosceles_triangle_property_angle_equal(1,ACB)
triangle_property_angle_sum(1,BAC)
parallelogram_property_opposite_angle_equal(1,EDCB)
Problem: As shown in the diagram, ∠DCE=80°, AD and BC are opposite sides of the ▱ ABCD. Find the measure of ∠DAB.
问题：如图所示，∠DCE=80°，BA和CD是平行四边形ABCD的一组对边。求∠DAB的大小。
Construction (CDL):
Shape(AB,BC,CD,DA)
Shape(DC,CE)
Collinear(BCE)
Conditions (CDL):
Equal(MeasureOfAngle(DCE),80)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(DAB))
Answer: 100
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,ABCD)
adjacent_complementary_angle(1,BCD,DCE)
Problem: As shown in the diagram, ∠DAB=60°, DC and AB are opposite sides of the ▱ CDAB, BF⊥DF, DE is perpendicular to CE. Find the measure of ∠FHE.
问题：如图所示，∠DAB=60°，CDAB是▱，BF⊥DF，DE⊥CE。求∠FHE的大小。
Construction (CDL):
Shape(CF,FH,HE,EC)
Shape(BE,EH,HB)
Shape(HF,FD,DH)
Shape(BH,HD,DA,AB)
Collinear(CEB)
Collinear(CFD)
Collinear(EHD)
Collinear(BHF)
Conditions (CDL):
Equal(MeasureOfAngle(DAB),60)
Parallelogram(CDAB)
PerpendicularBetweenLine(BF,DF)
PerpendicularBetweenLine(DE,CE)
Goal: Value(MeasureOfAngle(FHE))
Answer: 120
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,CDAB)
adjacent_complementary_angle(1,CFH,HFD)
quadrilateral_property_angle_sum(1,CFHE)
Problem: As shown in the diagram, ∠DAB=100°, AD and BC are opposite sides of the ▱ ABCD. Find the measure of ∠DCE.
问题：如图所示，∠DAB=100°，AD和BC是▱ABCD的一组对边。求∠DCE的大小。
Construction (CDL):
Shape(AB,BC,CD,DA)
Shape(DC,CE)
Collinear(BCE)
Conditions (CDL):
Equal(MeasureOfAngle(DAB),100)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(DCE))
Answer: 80
Theorem sequence:
adjacent_complementary_angle(1,BCD,DCE)
parallelogram_property_opposite_angle_equal(1,ABCD)
Problem: As shown in the diagram, ∠OAB=80°, OD is the angle bisector of ∠FOC, F is the midpoint of segment AD, AD and BC are opposite sides of the parallelogram ABCD. Find the measure of ∠ABD.
问题：如图所示，∠OAB=80°，OD平分∠FOC，F平分线段AD，BA和CD是▱ABCD的一组对边。求∠ABD的大小。
Construction (CDL):
Shape(AB,BO,OA)
Shape(FA,AO,OF)
Shape(FO,OD,DF)
Shape(DO,OC,CD)
Shape(OB,BC,CO)
Collinear(AOC)
Collinear(BOD)
Collinear(AFD)
Conditions (CDL):
Equal(MeasureOfAngle(OAB),80)
IsBisectorOfAngle(OD,FOC)
IsMidpointOfLine(F,AD)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(ABD))
Answer: 50
Theorem sequence:
parallelogram_property_diagonal_bisection(1,ABCD,O)
parallelogram_property_diagonal_bisection(1,BCDA,O)
parallel_property_alternate_interior_angle(2,BA,CD)
midsegment_of_triangle_judgment_midpoint(1,FO,DAB)
midsegment_of_triangle_judgment_midpoint(1,OF,ACD)
midsegment_of_triangle_property_parallel(1,FO,DAB)
midsegment_of_triangle_property_parallel(1,OF,ACD)
parallel_property_corresponding_angle(1,OF,CD,A)
parallel_property_corresponding_angle(2,BA,OF,D)
adjacent_complementary_angle(1,AOF,FOC)
angle_addition(1,FOD,DOC)
Problem: As shown in the diagram, ∠DBE=70°, ∠ECF=50°, D is the midpoint of segment AB, E is the midpoint of segment BC, F is the midpoint of segment AC. Find the measure of ∠DEF.
问题：如图所示，∠DBE=70°，∠ECF=50°，D是线段AB的中点，E是线段BC的中点，F是线段AC的中点。求∠DEF的大小。
Construction (CDL):
Shape(AD,DE,EF,FA)
Shape(DB,BE,ED)
Shape(FE,EC,CF)
Collinear(ADB)
Collinear(AFC)
Collinear(BEC)
Conditions (CDL):
Equal(MeasureOfAngle(DBE),70)
Equal(MeasureOfAngle(ECF),50)
IsMidpointOfLine(D,AB)
IsMidpointOfLine(E,BC)
IsMidpointOfLine(F,AC)
Goal: Value(MeasureOfAngle(DEF))
Answer: 60
Theorem sequence:
triangle_property_angle_sum(1,BCA)
midsegment_of_triangle_judgment_midpoint(1,ED,BCA)
midsegment_of_triangle_judgment_midpoint(1,FE,CAB)
midsegment_of_triangle_property_parallel(1,ED,BCA)
midsegment_of_triangle_property_parallel(1,FE,CAB)
parallel_property_collinear_extend(3,AC,DE,F)
parallel_property_collinear_extend(3,BA,EF,D)
parallelogram_judgment_parallel_and_parallel(1,ADEF)
parallelogram_property_opposite_angle_equal(1,ADEF)
Problem: As shown in the diagram, Add(MeasureOfAngle(DAB)=MeasureOfAngle(BCD)), BA and CD are opposite sides of the ▱ ABCD. Find the measure of ∠ABC.
问题：如图所示，Add(MeasureOfAngle(DAB)=MeasureOfAngle(BCD))，BA和CD是平行四边形ABCD的一组对边。求∠ABC的大小。
Construction (CDL):
Shape(DA,AB,BC,CD)
Conditions (CDL):
Equal(Add(MeasureOfAngle(DAB),MeasureOfAngle(BCD)),140)
Parallelogram(ABCD)
Goal: Value(MeasureOfAngle(ABC))
Answer: 110
Theorem sequence:
parallelogram_property_opposite_angle_equal(1,ABCD)
parallel_property_ipsilateral_internal_angle(1,BA,CD)