images
images listlengths 1
1
| problem
stringlengths 215
580
| answer
stringlengths 75
1.18k
| proID
stringlengths 1
4
|
|---|---|---|---|
<image>The Caption of this geometric diagram is:As shown in the diagram, triangle RST is congruent to triangle XYZ, TR=x+21, ZX=2*x-14, ∠TRS=4*y-10°, ∠ZXY=3*y+5°. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(RS,ST,TR)', 'Shape(XY,YZ,ZX)'], imgCDL:['Equal(LengthOfLine(TR),x+21)', 'Equal(LengthOfLine(ZX),2*x-14)', 'Equal(MeasureOfAngle(TRS),4*y-10)', 'Equal(MeasureOfAngle(ZXY),3*y+5)'], textCDL:['CongruentBetweenTriangle(RST,XYZ)', 'Equal(LengthOfLine(TR),x+21)', 'Equal(LengthOfLine(ZX),2*x-14)', 'Equal(MeasureOfAngle(TRS),4*y-10)', 'Equal(MeasureOfAngle(ZXY),3*y+5)'].
|
1
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, MN=3*x-4, NQ=15, PN=2*y+5, PQ=12, RM=18, RP=20, RQ=3*z-3, ∠MRQ=38°, ∠NQP=83°, ∠QNM=33°, MN and RP are opposite sides of the ▱ MRPN. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(MR,RQ,QM)', 'Shape(QR,RP,PQ)', 'Shape(MQ,QN,NM)', 'Shape(QP,PN,NQ)', 'Collinear(MQP)', 'Collinear(RQN)'], imgCDL:['Equal(LengthOfLine(MN),3*x-4)', 'Equal(LengthOfLine(NQ),15)', 'Equal(LengthOfLine(PN),2*y+5)', 'Equal(LengthOfLine(PQ),12)', 'Equal(LengthOfLine(RM),18)', 'Equal(LengthOfLine(RP),20)', 'Equal(LengthOfLine(RQ),3*z-3)', 'Equal(MeasureOfAngle(MRQ),38)', 'Equal(MeasureOfAngle(NQP),83)', 'Equal(MeasureOfAngle(QNM),33)'], textCDL:['Equal(LengthOfLine(MN),3*x-4)', 'Equal(LengthOfLine(NQ),15)', 'Equal(LengthOfLine(PN),2*y+5)', 'Equal(LengthOfLine(PQ),12)', 'Equal(LengthOfLine(RM),18)', 'Equal(LengthOfLine(RP),20)', 'Equal(LengthOfLine(RQ),3*z-3)', 'Equal(MeasureOfAngle(MRQ),38)', 'Equal(MeasureOfAngle(NQP),83)', 'Equal(MeasureOfAngle(QNM),33)', 'Parallelogram(MRPN)'].
|
2
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, BT=SB, QA=RA, QT=86, RS=54, the midsegment of quadrilateral AQTB is JK. Find JK. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(RA,AB,BS,SR)', 'Shape(AJ,JK,KB,BA)', 'Shape(JQ,QT,TK,KJ)', 'Collinear(RAJQ)', 'Collinear(SBKT)'], imgCDL:['Equal(LengthOfLine(BT),LengthOfLine(SB))', 'Equal(LengthOfLine(QA),LengthOfLine(RA))', 'Equal(LengthOfLine(QT),86)', 'Equal(LengthOfLine(RS),54)'], textCDL:['Equal(LengthOfLine(BT),LengthOfLine(SB))', 'Equal(LengthOfLine(QA),LengthOfLine(RA))', 'Equal(LengthOfLine(QT),86)', 'Equal(LengthOfLine(RS),54)', 'IsMidsegmentOfQuadrilateral(JK,AQTB)'].
|
3
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, WZ=23, XY=23, ∠ZWX=112°, XW is parallel to YZ, XYZW is a trapezoid. Find the measure of ∠YZW. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(WX,XY,YZ,ZW)'], imgCDL:['Equal(LengthOfLine(WZ),23)', 'Equal(LengthOfLine(XY),23)', 'Equal(MeasureOfAngle(ZWX),112)', 'ParallelBetweenLine(XW,YZ)'], textCDL:['Equal(LengthOfLine(WZ),23)', 'Equal(LengthOfLine(XY),23)', 'Equal(MeasureOfAngle(ZWX),112)', 'ParallelBetweenLine(XW,YZ)', 'Trapezoid(XYZW)'].
|
4
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=20, CM=12, MB=30, CM is perpendicular to AM. Find the perimeter of triangle AMB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AC,CM,MA)', 'Shape(AM,MB,BA)', 'Collinear(CMB)'], imgCDL:['Equal(LengthOfLine(AC),20)', 'Equal(LengthOfLine(CM),12)', 'Equal(LengthOfLine(MB),30)', 'PerpendicularBetweenLine(CM,AM)'], textCDL:['Equal(LengthOfLine(AC),20)', 'Equal(LengthOfLine(CM),12)', 'Equal(LengthOfLine(MB),30)', 'PerpendicularBetweenLine(CM,AM)'].
|
6
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=4/7, AC=x, BC=5/7, BA⊥CA. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AC,CB,BA)'], imgCDL:['Equal(LengthOfLine(AB),4/7)', 'Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLine(BC),5/7)', 'PerpendicularBetweenLine(BA,CA)'], textCDL:['Equal(LengthOfLine(AB),4/7)', 'Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLine(BC),5/7)', 'PerpendicularBetweenLine(BA,CA)'].
|
8
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, JK=10, MN=16, ∠KMN=98°, K is the center of ⊙K, MP is perpendicular to KP. Find the length of line LN. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(KJM,MK,KJ)', 'Shape(MP,PK,KM)', 'Shape(KML,LP,PM)', 'Shape(PL,LN,NP)', 'Shape(KLN,NL)', 'Shape(PN,KNJ,JK,KP)', 'Collinear(JKPL)', 'Collinear(MPN)', 'Cocircular(K,JMLN)'], imgCDL:['Equal(LengthOfLine(JK),10)', 'Equal(LengthOfLine(MN),16)', 'Equal(MeasureOfArc(KMN),98)', 'PerpendicularBetweenLine(MP,KP)'], textCDL:['Equal(LengthOfLine(JK),10)', 'Equal(LengthOfLine(MN),16)', 'Equal(MeasureOfArc(KMN),98)', 'IsCentreOfCircle(K,K)', 'PerpendicularBetweenLine(MP,KP)'].
|
9
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠FCD=x°, ∠EDB=10*x°, ∠EFD=40°, E is the center of ⊙E, CD is the tangent to circle E. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(EDB,BF,EFD)', 'Shape(CD,EFD,FC)', 'Shape(FB,EBF)', 'Collinear(BFC)', 'Cocircular(E,FDB)'], imgCDL:['Equal(MeasureOfAngle(FCD),x)', 'Equal(MeasureOfArc(EDB),10*x)', 'Equal(MeasureOfArc(EFD),40)'], textCDL:['Equal(MeasureOfAngle(FCD),x)', 'Equal(MeasureOfArc(EDB),10*x)', 'Equal(MeasureOfArc(EFD),40)', 'IsCentreOfCircle(E,E)', 'IsTangentOfCircle(CD,E)'].
|
10
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CFK=28°, ∠GKF=35°, ∠KAC=25°, ∠KHC=51°, EG is perpendicular to FG, HC is perpendicular to KC, KF is perpendicular to EF. Find ∠FEK. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(KA,AH,HK)', 'Shape(KH,HC,CK)', 'Shape(KC,CF,FK)', 'Shape(KF,FG,GK)', 'Shape(GF,FE,EG)', 'Collinear(AHCF)', 'Collinear(EGK)'], imgCDL:['Equal(MeasureOfAngle(CFK),28)', 'Equal(MeasureOfAngle(GKF),35)', 'Equal(MeasureOfAngle(KAC),25)', 'Equal(MeasureOfAngle(KHC),51)', 'PerpendicularBetweenLine(EG,FG)', 'PerpendicularBetweenLine(HC,KC)', 'PerpendicularBetweenLine(KF,EF)'], textCDL:['Equal(MeasureOfAngle(CFK),28)', 'Equal(MeasureOfAngle(GKF),35)', 'Equal(MeasureOfAngle(KAC),25)', 'Equal(MeasureOfAngle(KHC),51)', 'PerpendicularBetweenLine(EG,FG)', 'PerpendicularBetweenLine(HC,KC)', 'PerpendicularBetweenLine(KF,EF)'].
|
11
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=30, CD=30, ∠XCZ=40°, X is the center of circle X, AM⊥YM, DN is perpendicular to ZN. Find the measure of arc XBA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(XBY,YM,MB)', 'Shape(XYA,AM,MY)', 'Shape(XM,MA,XAC,CN,NX)', 'Shape(NC,XCZ,ZN)', 'Shape(NZ,XZD,DN)', 'Shape(MX,XN,ND,XDB,BM)', 'Collinear(AMB)', 'Collinear(YMX)', 'Collinear(XNZ)', 'Collinear(CND)', 'Cocircular(X,ACZDBY)'], imgCDL:['Equal(LengthOfLine(AB),30)', 'Equal(LengthOfLine(CD),30)', 'Equal(MeasureOfArc(XCZ),40)', 'PerpendicularBetweenLine(AM,YM)', 'PerpendicularBetweenLine(DN,ZN)'], textCDL:['Equal(LengthOfLine(AB),30)', 'Equal(LengthOfLine(CD),30)', 'Equal(MeasureOfArc(XCZ),40)', 'IsCentreOfCircle(X,X)', 'PerpendicularBetweenLine(AM,YM)', 'PerpendicularBetweenLine(DN,ZN)'].
|
12
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AJ=2*x+3, CJ=8*y-36, JB=5*x, JD=4*y, AD and CB are opposite sides of the parallelogram ACBD. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AC,CJ,JA)', 'Shape(JC,CB,BJ)', 'Shape(AJ,JD,DA)', 'Shape(JB,BD,DJ)', 'Collinear(AJB)', 'Collinear(CJD)'], imgCDL:['Equal(LengthOfLine(AJ),2*x+3)', 'Equal(LengthOfLine(CJ),8*y-36)', 'Equal(LengthOfLine(JB),5*x)', 'Equal(LengthOfLine(JD),4*y)'], textCDL:['Equal(LengthOfLine(AJ),2*x+3)', 'Equal(LengthOfLine(CJ),8*y-36)', 'Equal(LengthOfLine(JB),5*x)', 'Equal(LengthOfLine(JD),4*y)', 'Parallelogram(ACBD)'].
|
14
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, IB=1/2*x-7, JI=1/4*x+5, LD=66-2/3*y, NL=1/3*y-6, NL=LD, CJ is perpendicular to NJ, IB⊥DB, JI⊥LI. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(JI,IL,LN,NJ)', 'Shape(IB,BD,DL,LI)', 'Shape(CJ,JN)', 'Collinear(CJIB)', 'Collinear(NLD)'], imgCDL:['Equal(LengthOfLine(IB),1/2*x-7)', 'Equal(LengthOfLine(JI),1/4*x+5)', 'Equal(LengthOfLine(LD),66-2/3*y)', 'Equal(LengthOfLine(NL),1/3*y-6)', 'Equal(LengthOfLine(NL),LengthOfLine(LD))', 'PerpendicularBetweenLine(CJ,NJ)', 'PerpendicularBetweenLine(IB,DB)', 'PerpendicularBetweenLine(JI,LI)'], textCDL:['Equal(LengthOfLine(IB),1/2*x-7)', 'Equal(LengthOfLine(JI),1/4*x+5)', 'Equal(LengthOfLine(LD),66-2/3*y)', 'Equal(LengthOfLine(NL),1/3*y-6)', 'Equal(LengthOfLine(NL),LengthOfLine(LD))', 'PerpendicularBetweenLine(CJ,NJ)', 'PerpendicularBetweenLine(IB,DB)', 'PerpendicularBetweenLine(JI,LI)'].
|
15
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=10, AC=y, BC=x, ∠ABC=60°, BC is perpendicular to AC. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AB,BC,CA)'], imgCDL:['Equal(LengthOfLine(AB),10)', 'Equal(LengthOfLine(AC),y)', 'Equal(LengthOfLine(BC),x)', 'Equal(MeasureOfAngle(ABC),60)', 'PerpendicularBetweenLine(BC,AC)'], textCDL:['Equal(LengthOfLine(AB),10)', 'Equal(LengthOfLine(AC),y)', 'Equal(LengthOfLine(BC),x)', 'Equal(MeasureOfAngle(ABC),60)', 'PerpendicularBetweenLine(BC,AC)'].
|
16
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=8, AD=27, AE=12, CD is parallel to BE. Find BC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(CB,BE,ED,DC)', 'Shape(BA,AE,EB)', 'Collinear(ABC)', 'Collinear(AED)'], imgCDL:['Equal(LengthOfLine(AB),8)', 'Equal(LengthOfLine(AD),27)', 'Equal(LengthOfLine(AE),12)', 'ParallelBetweenLine(CD,BE)'], textCDL:['Equal(LengthOfLine(AB),8)', 'Equal(LengthOfLine(AD),27)', 'Equal(LengthOfLine(AE),12)', 'ParallelBetweenLine(CD,BE)'].
|
17
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=4*x-17, CD=2*x-1, ∠BCD=4*y-19°, ∠CBA=3*y+3°, ACDB is a parallelogram. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AC,CB,BA)', 'Shape(BC,CD,DB)'], imgCDL:['Equal(LengthOfLine(AB),4*x-17)', 'Equal(LengthOfLine(CD),2*x-1)', 'Equal(MeasureOfAngle(BCD),4*y-19)', 'Equal(MeasureOfAngle(CBA),3*y+3)'], textCDL:['Equal(LengthOfLine(AB),4*x-17)', 'Equal(LengthOfLine(CD),2*x-1)', 'Equal(MeasureOfAngle(BCD),4*y-19)', 'Equal(MeasureOfAngle(CBA),3*y+3)', 'Parallelogram(ACDB)'].
|
19
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AE=BE, BA=8, BC=8, BE=CE, DA=10, DC=10, ∠ADE=x°, DE is perpendicular to AE. Find sin(x). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AD,DE,EA)', 'Shape(AE,EB,BA)', 'Shape(ED,DC,CE)', 'Shape(BE,EC,CB)', 'Collinear(DEB)', 'Collinear(AEC)'], imgCDL:['Equal(LengthOfLine(AE),LengthOfLine(BE))', 'Equal(LengthOfLine(BA),8)', 'Equal(LengthOfLine(BC),8)', 'Equal(LengthOfLine(BE),LengthOfLine(CE))', 'Equal(LengthOfLine(DA),10)', 'Equal(LengthOfLine(DC),10)', 'Equal(MeasureOfAngle(ADE),x)', 'PerpendicularBetweenLine(DE,AE)'], textCDL:['Equal(LengthOfLine(AE),LengthOfLine(BE))', 'Equal(LengthOfLine(BA),8)', 'Equal(LengthOfLine(BC),8)', 'Equal(LengthOfLine(BE),LengthOfLine(CE))', 'Equal(LengthOfLine(DA),10)', 'Equal(LengthOfLine(DC),10)', 'Equal(MeasureOfAngle(ADE),x)', 'PerpendicularBetweenLine(DE,AE)'].
|
20
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABX=5*y-6°, ∠BXC=2*x+24°, ∠CAB=3*x-17°, ∠XCA=y+58°, quadrilateral ABXC is a ▱. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AB,BX,XC,CA)'], imgCDL:['Equal(MeasureOfAngle(ABX),5*y-6)', 'Equal(MeasureOfAngle(BXC),2*x+24)', 'Equal(MeasureOfAngle(CAB),3*x-17)', 'Equal(MeasureOfAngle(XCA),y+58)'], textCDL:['Equal(MeasureOfAngle(ABX),5*y-6)', 'Equal(MeasureOfAngle(BXC),2*x+24)', 'Equal(MeasureOfAngle(CAB),3*x-17)', 'Equal(MeasureOfAngle(XCA),y+58)', 'Parallelogram(ABXC)'].
|
21
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠NJK=101°, JA∥NF. Find ∠HNJ. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(KJ,JE)', 'Shape(EJ,JA)', 'Shape(AJ,JN)', 'Shape(NJ,JK)', 'Shape(HN,NJ)', 'Shape(JN,NF)', 'Shape(FN,NI)', 'Shape(IN,NH)', 'Collinear(KJA)', 'Collinear(HNF)', 'Collinear(EJNI)'], imgCDL:['Equal(MeasureOfAngle(NJK),101)', 'ParallelBetweenLine(JA,NF)'], textCDL:['Equal(MeasureOfAngle(NJK),101)', 'ParallelBetweenLine(JA,NF)'].
|
22
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, SR=3*x-5, TR=2*x+7, TS=22, ∠RST=∠STR. Find RS. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(RS,ST,TR)'], imgCDL:['Equal(LengthOfLine(SR),3*x-5)', 'Equal(LengthOfLine(TR),2*x+7)', 'Equal(LengthOfLine(TS),22)'], textCDL:['Equal(LengthOfLine(SR),3*x-5)', 'Equal(LengthOfLine(TR),2*x+7)', 'Equal(LengthOfLine(TS),22)', 'Equal(MeasureOfAngle(RST),MeasureOfAngle(STR))'].
|
23
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, YX=24, YZ=28, ∠XWZ=105°, WZYX is a parallelogram. Find ∠WZY. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(WZ,ZY,YX,XW)'], imgCDL:['Equal(LengthOfLine(YX),24)', 'Equal(LengthOfLine(YZ),28)', 'Equal(MeasureOfAngle(XWZ),105)'], textCDL:['Equal(LengthOfLine(YX),24)', 'Equal(LengthOfLine(YZ),28)', 'Equal(MeasureOfAngle(XWZ),105)', 'Parallelogram(WZYX)'].
|
24
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=x, AD=3*sqrt(3), BD=9, CD=y, ∠ABC=30°, ∠BCA=60°, AD is perpendicular to CD, CA is perpendicular to BA. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(CA,AD,DC)', 'Shape(DA,AB,BD)', 'Collinear(BDC)'], imgCDL:['Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(AD),3*sqrt(3))', 'Equal(LengthOfLine(BD),9)', 'Equal(LengthOfLine(CD),y)', 'Equal(MeasureOfAngle(ABC),30)', 'Equal(MeasureOfAngle(BCA),60)', 'PerpendicularBetweenLine(AD,CD)', 'PerpendicularBetweenLine(CA,BA)'], textCDL:['Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(AD),3*sqrt(3))', 'Equal(LengthOfLine(BD),9)', 'Equal(LengthOfLine(CD),y)', 'Equal(MeasureOfAngle(ABC),30)', 'Equal(MeasureOfAngle(BCA),60)', 'PerpendicularBetweenLine(AD,CD)', 'PerpendicularBetweenLine(CA,BA)'].
|
25
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=y, AC=x, BC=18, ∠ABC=30°, CA is perpendicular to BA. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AB,BC,CA)'], imgCDL:['Equal(LengthOfLine(AB),y)', 'Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLine(BC),18)', 'Equal(MeasureOfAngle(ABC),30)', 'PerpendicularBetweenLine(CA,BA)'], textCDL:['Equal(LengthOfLine(AB),y)', 'Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLine(BC),18)', 'Equal(MeasureOfAngle(ABC),30)', 'PerpendicularBetweenLine(CA,BA)'].
|
26
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CHE=9*x-11°, ∠GDF=8*x+4°, BD∥EH. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(GD,DF)', 'Shape(FD,DH)', 'Shape(DH,HA)', 'Shape(AH,HC)', 'Shape(CH,HE)', 'Shape(EH,HD)', 'Shape(HD,DB)', 'Shape(BD,DG)', 'Collinear(GDHC)', 'Collinear(FDB)', 'Collinear(AHE)'], imgCDL:['Equal(MeasureOfAngle(CHE),9*x-11)', 'Equal(MeasureOfAngle(GDF),8*x+4)', 'ParallelBetweenLine(BD,EH)'], textCDL:['Equal(MeasureOfAngle(CHE),9*x-11)', 'Equal(MeasureOfAngle(GDF),8*x+4)', 'ParallelBetweenLine(BD,EH)'].
|
28
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, RS=5, TR=6, TS=3, ∠SRT=x°. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(SR,RT,TS)'], imgCDL:['Equal(LengthOfLine(RS),5)', 'Equal(LengthOfLine(TR),6)', 'Equal(LengthOfLine(TS),3)', 'Equal(MeasureOfAngle(SRT),x)'], textCDL:['Equal(LengthOfLine(RS),5)', 'Equal(LengthOfLine(TR),6)', 'Equal(LengthOfLine(TS),3)', 'Equal(MeasureOfAngle(SRT),x)'].
|
29
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=2*x+3, BC=5*x, DA=DC, quadrilateral ADCB is a parallelogram. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AD,DE,EA)', 'Shape(ED,DC,CE)', 'Shape(EC,CB,BE)', 'Shape(BA,AE,EB)', 'Collinear(AEC)', 'Collinear(DEB)'], imgCDL:['Equal(LengthOfLine(AB),2*x+3)', 'Equal(LengthOfLine(BC),5*x)'], textCDL:['Equal(LengthOfLine(AB),2*x+3)', 'Equal(LengthOfLine(BC),5*x)', 'Equal(LengthOfLine(DA),LengthOfLine(DC))', 'Parallelogram(ADCB)'].
|
33
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABD=130°, ∠CBA=x°, ∠DBC=95°. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BAC,CB,BA)', 'Shape(BDA,AB,BD)', 'Shape(BCD,DB,BC)'], imgCDL:['Equal(MeasureOfAngle(ABD),130)', 'Equal(MeasureOfAngle(CBA),x)', 'Equal(MeasureOfAngle(DBC),95)'], textCDL:['Equal(MeasureOfAngle(ABD),130)', 'Equal(MeasureOfAngle(CBA),x)', 'Equal(MeasureOfAngle(DBC),95)'].
|
36
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=y, AC=8, BC=x, ∠BAC=60°, AC is perpendicular to BC. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AC,CB,BA)'], imgCDL:['Equal(LengthOfLine(AB),y)', 'Equal(LengthOfLine(AC),8)', 'Equal(LengthOfLine(BC),x)', 'Equal(MeasureOfAngle(BAC),60)', 'PerpendicularBetweenLine(AC,BC)'], textCDL:['Equal(LengthOfLine(AB),y)', 'Equal(LengthOfLine(AC),8)', 'Equal(LengthOfLine(BC),x)', 'Equal(MeasureOfAngle(BAC),60)', 'PerpendicularBetweenLine(AC,BC)'].
|
38
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, EJ=6, LK=7, ML=4, quadrilateral JMLK is a ▱, JE is perpendicular to LE. Find the perimeter of quadrilateral JMLK. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(JM,ME,EJ)', 'Shape(JE,EL,LK,KJ)', 'Collinear(MEL)'], imgCDL:['Equal(LengthOfLine(EJ),6)', 'Equal(LengthOfLine(LK),7)', 'Equal(LengthOfLine(ML),4)', 'PerpendicularBetweenLine(JE,LE)'], textCDL:['Equal(LengthOfLine(EJ),6)', 'Equal(LengthOfLine(LK),7)', 'Equal(LengthOfLine(ML),4)', 'Parallelogram(JMLK)', 'PerpendicularBetweenLine(JE,LE)'].
|
39
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=8, AC=14, BC=8, BX=x, BX⊥CX. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BA,AX,XB)', 'Shape(BX,XC,CB)', 'Collinear(AXC)'], imgCDL:['Equal(LengthOfLine(AB),8)', 'Equal(LengthOfLine(AC),14)', 'Equal(LengthOfLine(BC),8)', 'Equal(LengthOfLine(BX),x)', 'PerpendicularBetweenLine(BX,CX)'], textCDL:['Equal(LengthOfLine(AB),8)', 'Equal(LengthOfLine(AC),14)', 'Equal(LengthOfLine(BC),8)', 'Equal(LengthOfLine(BX),x)', 'PerpendicularBetweenLine(BX,CX)'].
|
40
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, NM=4, ∠NLM=∠PLN, ∠PLN=25°, LM is perpendicular to NM, NP is perpendicular to LP. Find ∠MNP. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(LM,MN,NL)', 'Shape(LN,NP,PL)'], imgCDL:['Equal(LengthOfLine(NM),4)', 'Equal(MeasureOfAngle(NLM),MeasureOfAngle(PLN))', 'Equal(MeasureOfAngle(PLN),25)', 'PerpendicularBetweenLine(LM,NM)', 'PerpendicularBetweenLine(NP,LP)'], textCDL:['Equal(LengthOfLine(NM),4)', 'Equal(MeasureOfAngle(NLM),MeasureOfAngle(PLN))', 'Equal(MeasureOfAngle(PLN),25)', 'PerpendicularBetweenLine(LM,NM)', 'PerpendicularBetweenLine(NP,LP)'].
|
41
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ML=w, MN=2*y+5, MR=4*x-2, QL=12, QN=3*x+2, QR=3*y, quadrilateral NMRQ is a ▱. Find the value of w. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(NM,ML,LN)', 'Shape(LM,MR,RL)', 'Shape(NL,LQ,QN)', 'Shape(LR,RQ,QL)', 'Collinear(NLR)', 'Collinear(MLQ)'], imgCDL:['Equal(LengthOfLine(ML),w)', 'Equal(LengthOfLine(MN),2*y+5)', 'Equal(LengthOfLine(MR),4*x-2)', 'Equal(LengthOfLine(QL),12)', 'Equal(LengthOfLine(QN),3*x+2)', 'Equal(LengthOfLine(QR),3*y)'], textCDL:['Equal(LengthOfLine(ML),w)', 'Equal(LengthOfLine(MN),2*y+5)', 'Equal(LengthOfLine(MR),4*x-2)', 'Equal(LengthOfLine(QL),12)', 'Equal(LengthOfLine(QN),3*x+2)', 'Equal(LengthOfLine(QR),3*y)', 'Parallelogram(NMRQ)'].
|
43
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, BA=6, CA=x, CB=x, ∠BAC=45°, ∠CBA=45°, AC is perpendicular to BC. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(CB,BA,AC)'], imgCDL:['Equal(LengthOfLine(BA),6)', 'Equal(LengthOfLine(CA),x)', 'Equal(LengthOfLine(CB),x)', 'Equal(MeasureOfAngle(BAC),45)', 'Equal(MeasureOfAngle(CBA),45)', 'PerpendicularBetweenLine(AC,BC)'], textCDL:['Equal(LengthOfLine(BA),6)', 'Equal(LengthOfLine(CA),x)', 'Equal(LengthOfLine(CB),x)', 'Equal(MeasureOfAngle(BAC),45)', 'Equal(MeasureOfAngle(CBA),45)', 'PerpendicularBetweenLine(AC,BC)'].
|
44
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠EYQ=3*y+1°, ∠MAQ=3*x+11°, ∠YQF=4*x-5°, EF is parallel to YQ, QA is parallel to YM, YQ∥MA. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(EY,YQ,QF,FE)', 'Shape(YM,MA,AQ,QY)', 'Collinear(EYM)', 'Collinear(FQA)'], imgCDL:['Equal(MeasureOfAngle(EYQ),3*y+1)', 'Equal(MeasureOfAngle(MAQ),3*x+11)', 'Equal(MeasureOfAngle(YQF),4*x-5)', 'ParallelBetweenLine(EF,YQ)', 'ParallelBetweenLine(QA,YM)', 'ParallelBetweenLine(YQ,MA)'], textCDL:['Equal(MeasureOfAngle(EYQ),3*y+1)', 'Equal(MeasureOfAngle(MAQ),3*x+11)', 'Equal(MeasureOfAngle(YQF),4*x-5)', 'ParallelBetweenLine(EF,YQ)', 'ParallelBetweenLine(QA,YM)', 'ParallelBetweenLine(YQ,MA)'].
|
48
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, FE=6, FG=3, FH=4, HG=2, △DEF is similar to △GFH.. Find Perimeter(△DEF). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(DE,EF,FD)', 'Shape(CD,DF,FG,GC)', 'Shape(GF,FH,HG)', 'Collinear(CDE)', 'Collinear(EFH)', 'Collinear(HGC)'], imgCDL:['Equal(LengthOfLine(FE),6)', 'Equal(LengthOfLine(FG),3)', 'Equal(LengthOfLine(FH),4)', 'Equal(LengthOfLine(HG),2)'], textCDL:['Equal(LengthOfLine(FE),6)', 'Equal(LengthOfLine(FG),3)', 'Equal(LengthOfLine(FH),4)', 'Equal(LengthOfLine(HG),2)', 'SimilarBetweenTriangle(DEF,GFH)'].
|
50
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠LWX=3*a+40°, ∠WXE=2*a+25°, ∠XZK=5*b-26°, WL∥XE, XN is parallel to ZK. Find the value of a. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(GW,WL)', 'Shape(LW,WX)', 'Shape(WX,XE)', 'Shape(EX,XN)', 'Shape(NX,XZ)', 'Shape(XZ,ZK)', 'Shape(KZ,ZH)', 'Shape(HZ,ZY)', 'Shape(ZY,YM)', 'Shape(MY,YI)', 'Shape(IY,YW)', 'Shape(YW,WG)', 'Shape(WY,YZ,ZX,XW)', 'Collinear(GWXN)', 'Collinear(IYZK)', 'Collinear(LWYM)', 'Collinear(EXZH)'], imgCDL:['Equal(MeasureOfAngle(LWX),3*a+40)', 'Equal(MeasureOfAngle(WXE),2*a+25)', 'Equal(MeasureOfAngle(XZK),5*b-26)', 'ParallelBetweenLine(WL,XE)', 'ParallelBetweenLine(XN,ZK)'], textCDL:['Equal(MeasureOfAngle(LWX),3*a+40)', 'Equal(MeasureOfAngle(WXE),2*a+25)', 'Equal(MeasureOfAngle(XZK),5*b-26)', 'ParallelBetweenLine(WL,XE)', 'ParallelBetweenLine(XN,ZK)'].
|
51
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AGC=40°, ∠DGF=53°, CB⊥GB, FG is perpendicular to CG, GF is perpendicular to DF. Find the measure of ∠FDG. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(DG,GF,FD)', 'Shape(FG,GA,AF)', 'Shape(BG,GC,CB)', 'Shape(AB,BC,CA)', 'Collinear(DFA)', 'Collinear(ABG)'], imgCDL:['Equal(MeasureOfAngle(AGC),40)', 'Equal(MeasureOfAngle(DGF),53)', 'PerpendicularBetweenLine(CB,GB)', 'PerpendicularBetweenLine(FG,CG)', 'PerpendicularBetweenLine(GF,DF)'], textCDL:['Equal(MeasureOfAngle(AGC),40)', 'Equal(MeasureOfAngle(DGF),53)', 'PerpendicularBetweenLine(CB,GB)', 'PerpendicularBetweenLine(FG,CG)', 'PerpendicularBetweenLine(GF,DF)'].
|
52
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠FOE=45°, the center of ⊙O is O, CO is perpendicular to AO, EO⊥BO. Find the measure of arc OAE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(OE,OEF,FO)', 'Shape(OF,OFA,AO)', 'Shape(OA,OAC,CO)', 'Shape(OC,OCB,BO)', 'Shape(OB,OBE,EO)', 'Collinear(EOC)', 'Collinear(AOB)', 'Cocircular(O,EFACB)'], imgCDL:['Equal(MeasureOfAngle(FOE),45)', 'PerpendicularBetweenLine(CO,AO)', 'PerpendicularBetweenLine(EO,BO)'], textCDL:['Equal(MeasureOfAngle(FOE),45)', 'IsCentreOfCircle(O,O)', 'PerpendicularBetweenLine(CO,AO)', 'PerpendicularBetweenLine(EO,BO)'].
|
53
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, BC=8, BH=12, O is the center of circle O, quadrilateral DCBH is a rectangle. Find the area of DCBH minus the area of the sector ODH. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(DC,CB,BH,ODH)', 'Shape(OD,ODH,HO)', 'Collinear(DOH)', 'Cocircular(O,DH)'], imgCDL:['Equal(LengthOfLine(BC),8)', 'Equal(LengthOfLine(BH),12)'], textCDL:['Equal(LengthOfLine(BC),8)', 'Equal(LengthOfLine(BH),12)', 'IsCentreOfCircle(O,O)', 'Rectangle(DCBH)'].
|
54
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=10, AC=6, BC=x, AC is perpendicular to BC. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AC,CB,BA)'], imgCDL:['Equal(LengthOfLine(AB),10)', 'Equal(LengthOfLine(AC),6)', 'Equal(LengthOfLine(BC),x)', 'PerpendicularBetweenLine(AC,BC)'], textCDL:['Equal(LengthOfLine(AB),10)', 'Equal(LengthOfLine(AC),6)', 'Equal(LengthOfLine(BC),x)', 'PerpendicularBetweenLine(AC,BC)'].
|
55
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=14, ∠ADB=30°, DP is perpendicular to AP, ADCB is a rhombus. Find CP. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AD,DP,PA)', 'Shape(PD,DC,CP)', 'Shape(PC,CB,BP)', 'Shape(AP,PB,BA)', 'Collinear(APC)', 'Collinear(DPB)'], imgCDL:['Equal(LengthOfLine(AB),14)', 'Equal(MeasureOfAngle(ADB),30)', 'PerpendicularBetweenLine(DP,AP)'], textCDL:['Equal(LengthOfLine(AB),14)', 'Equal(MeasureOfAngle(ADB),30)', 'PerpendicularBetweenLine(DP,AP)', 'Rhombus(ADCB)'].
|
57
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠BCE=∠EBC, ∠DAG=136°, ∠DEA=47°, ∠EFB=63°, ∠FED=69°. Find ∠EBC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(FB,BE,EF)', 'Shape(DE,EA,AD)', 'Shape(BC,CE,EB)', 'Shape(FE,ED)', 'Shape(FE,EA)', 'Shape(DA,AG)', 'Shape(AE,EC)', 'Collinear(BEAG)', 'Collinear(FEC)'], imgCDL:['Equal(MeasureOfAngle(BCE),MeasureOfAngle(EBC))', 'Equal(MeasureOfAngle(DAG),136)', 'Equal(MeasureOfAngle(DEA),47)', 'Equal(MeasureOfAngle(EFB),63)', 'Equal(MeasureOfAngle(FED),69)'], textCDL:['Equal(MeasureOfAngle(BCE),MeasureOfAngle(EBC))', 'Equal(MeasureOfAngle(DAG),136)', 'Equal(MeasureOfAngle(DEA),47)', 'Equal(MeasureOfAngle(EFB),63)', 'Equal(MeasureOfAngle(FED),69)'].
|
58
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠LWX=53°, WL is parallel to XE, XN is parallel to ZK. Find ∠XZK. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(GW,WL)', 'Shape(LW,WX)', 'Shape(WX,XE)', 'Shape(EX,XN)', 'Shape(NX,XZ)', 'Shape(XZ,ZK)', 'Shape(KZ,ZH)', 'Shape(HZ,ZY)', 'Shape(ZY,YM)', 'Shape(MY,YI)', 'Shape(IY,YW)', 'Shape(YW,WG)', 'Shape(WY,YZ,ZX,XW)', 'Collinear(GWXN)', 'Collinear(IYZK)', 'Collinear(LWYM)', 'Collinear(EXZH)'], imgCDL:['Equal(MeasureOfAngle(LWX),53)', 'ParallelBetweenLine(WL,XE)', 'ParallelBetweenLine(XN,ZK)'], textCDL:['Equal(MeasureOfAngle(LWX),53)', 'ParallelBetweenLine(WL,XE)', 'ParallelBetweenLine(XN,ZK)'].
|
59
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=x, AD=4, BC=y, BD=9, CD=z, AC⊥BC, BD is perpendicular to CD. Find the value of z. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AC,CD,DA)', 'Shape(DC,CB,BD)', 'Collinear(BDA)'], imgCDL:['Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLine(AD),4)', 'Equal(LengthOfLine(BC),y)', 'Equal(LengthOfLine(BD),9)', 'Equal(LengthOfLine(CD),z)', 'PerpendicularBetweenLine(AC,BC)', 'PerpendicularBetweenLine(BD,CD)'], textCDL:['Equal(LengthOfLine(AC),x)', 'Equal(LengthOfLine(AD),4)', 'Equal(LengthOfLine(BC),y)', 'Equal(LengthOfLine(BD),9)', 'Equal(LengthOfLine(CD),z)', 'PerpendicularBetweenLine(AC,BC)', 'PerpendicularBetweenLine(BD,CD)'].
|
60
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=8, CA=10, CB=a, ∠BAC=60°. Find the value of a. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AC,CB,BA)'], imgCDL:['Equal(LengthOfLine(AB),8)', 'Equal(LengthOfLine(CA),10)', 'Equal(LengthOfLine(CB),a)', 'Equal(MeasureOfAngle(BAC),60)'], textCDL:['Equal(LengthOfLine(AB),8)', 'Equal(LengthOfLine(CA),10)', 'Equal(LengthOfLine(CB),a)', 'Equal(MeasureOfAngle(BAC),60)'].
|
61
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CFD=x+36°, ∠DEC=2*y°, ∠ECF=78°, ∠FDE=110°, CE∥FD. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(EC,CF,FD,DE)'], imgCDL:['Equal(MeasureOfAngle(CFD),x+36)', 'Equal(MeasureOfAngle(DEC),2*y)', 'Equal(MeasureOfAngle(ECF),78)', 'Equal(MeasureOfAngle(FDE),110)', 'ParallelBetweenLine(CE,FD)'], textCDL:['Equal(MeasureOfAngle(CFD),x+36)', 'Equal(MeasureOfAngle(DEC),2*y)', 'Equal(MeasureOfAngle(ECF),78)', 'Equal(MeasureOfAngle(FDE),110)', 'ParallelBetweenLine(CE,FD)'].
|
63
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠AJH=x°, ∠HGB=2*x°, A is the center of ⊙A, GB is perpendicular to HB, JH is perpendicular to GH. Find the measure of ∠BHG. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AGF,FB,BG)', 'Shape(AB,BF,AFJ,JA)', 'Shape(BA,AJ,JH,HB)', 'Shape(AJH,HJ)', 'Shape(BH,HG,GB)', 'Shape(AHG,GH)', 'Collinear(FBH)', 'Collinear(GBAJ)', 'Cocircular(A,GFJH)'], imgCDL:['Equal(MeasureOfAngle(AJH),x)', 'Equal(MeasureOfAngle(HGB),2*x)', 'PerpendicularBetweenLine(GB,HB)', 'PerpendicularBetweenLine(JH,GH)'], textCDL:['Equal(MeasureOfAngle(AJH),x)', 'Equal(MeasureOfAngle(HGB),2*x)', 'IsCentreOfCircle(A,A)', 'PerpendicularBetweenLine(GB,HB)', 'PerpendicularBetweenLine(JH,GH)'].
|
64
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CBD=55°, ∠FBG=35°, the center of ⊙B is B. Find the measure of ⌒BCD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BC,BCA,AB)', 'Shape(BA,BAG,GB)', 'Shape(BG,BGF,FB)', 'Shape(BF,BFD,DB)', 'Shape(BD,BDC,CB)', 'Collinear(CBG)', 'Collinear(ABD)', 'Cocircular(B,AGFDC)'], imgCDL:['Equal(MeasureOfAngle(CBD),55)', 'Equal(MeasureOfAngle(FBG),35)'], textCDL:['Equal(MeasureOfAngle(CBD),55)', 'Equal(MeasureOfAngle(FBG),35)', 'IsCentreOfCircle(B,B)'].
|
65
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, BA=3*x-13, BC=2*x+5, ∠BCD=∠CDB, ∠BDA=∠DAB, ∠DBC=60°. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BC,CD,DB)', 'Shape(BD,DA,AB)'], imgCDL:['Equal(LengthOfLine(BA),3*x-13)', 'Equal(LengthOfLine(BC),2*x+5)', 'Equal(MeasureOfAngle(BCD),MeasureOfAngle(CDB))', 'Equal(MeasureOfAngle(BDA),MeasureOfAngle(DAB))', 'Equal(MeasureOfAngle(DBC),60)'], textCDL:['Equal(LengthOfLine(BA),3*x-13)', 'Equal(LengthOfLine(BC),2*x+5)', 'Equal(MeasureOfAngle(BCD),MeasureOfAngle(CDB))', 'Equal(MeasureOfAngle(BDA),MeasureOfAngle(DAB))', 'Equal(MeasureOfAngle(DBC),60)'].
|
66
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, QT=x, RQ=6, SQ=18, SR=14, ∠TRQ=∠SRT. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(QT,TR,RQ)', 'Shape(TS,SR,RT)', 'Collinear(QTS)'], imgCDL:['Equal(LengthOfLine(QT),x)', 'Equal(LengthOfLine(RQ),6)', 'Equal(LengthOfLine(SQ),18)', 'Equal(LengthOfLine(SR),14)', 'Equal(MeasureOfAngle(TRQ),MeasureOfAngle(SRT))'], textCDL:['Equal(LengthOfLine(QT),x)', 'Equal(LengthOfLine(RQ),6)', 'Equal(LengthOfLine(SQ),18)', 'Equal(LengthOfLine(SR),14)', 'Equal(MeasureOfAngle(TRQ),MeasureOfAngle(SRT))'].
|
67
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AD=5, BC=32, CD=12, AC is perpendicular to BC, BD is perpendicular to CD, triangle ACB is similar to triangle CBD.. Find Perimeter(△ACB). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AC,CD,DA)', 'Shape(DC,CB,BD)', 'Collinear(ADB)'], imgCDL:['Equal(LengthOfLine(AD),5)', 'Equal(LengthOfLine(BC),32)', 'Equal(LengthOfLine(CD),12)', 'PerpendicularBetweenLine(AC,BC)', 'PerpendicularBetweenLine(BD,CD)'], textCDL:['Equal(LengthOfLine(AD),5)', 'Equal(LengthOfLine(BC),32)', 'Equal(LengthOfLine(CD),12)', 'PerpendicularBetweenLine(AC,BC)', 'PerpendicularBetweenLine(BD,CD)', 'SimilarBetweenTriangle(ACB,CBD)'].
|
68
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DEF=25°, ∠GFD=65°, EG is perpendicular to DG. Find the measure of ∠FDG. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(DE,EG,GD)', 'Shape(DG,GF,FD)', 'Collinear(EGF)'], imgCDL:['Equal(MeasureOfAngle(DEF),25)', 'Equal(MeasureOfAngle(GFD),65)', 'PerpendicularBetweenLine(EG,DG)'], textCDL:['Equal(MeasureOfAngle(DEF),25)', 'Equal(MeasureOfAngle(GFD),65)', 'PerpendicularBetweenLine(EG,DG)'].
|
69
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠TYZ=52°, ∠ZYX=38°, TY is perpendicular to XY, XW is perpendicular to TW, YX is perpendicular to WX, YZ is perpendicular to TZ. Find ∠WTZ. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(TY,YZ,ZT)', 'Shape(TZ,ZW,WT)', 'Shape(ZY,YX,XW,WZ)', 'Collinear(YZW)'], imgCDL:['Equal(MeasureOfAngle(TYZ),52)', 'Equal(MeasureOfAngle(ZYX),38)', 'PerpendicularBetweenLine(TY,XY)', 'PerpendicularBetweenLine(XW,TW)', 'PerpendicularBetweenLine(YX,WX)', 'PerpendicularBetweenLine(YZ,TZ)'], textCDL:['Equal(MeasureOfAngle(TYZ),52)', 'Equal(MeasureOfAngle(ZYX),38)', 'PerpendicularBetweenLine(TY,XY)', 'PerpendicularBetweenLine(XW,TW)', 'PerpendicularBetweenLine(YX,WX)', 'PerpendicularBetweenLine(YZ,TZ)'].
|
72
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=y, AC=12, AD=BD, ∠CAB=x°, DB⊥CB, ADBC is a square. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AD,DB,BA)', 'Shape(AB,BC,CA)'], imgCDL:['Equal(LengthOfLine(AB),y)', 'Equal(LengthOfLine(AC),12)', 'Equal(LengthOfLine(AD),LengthOfLine(BD))', 'Equal(MeasureOfAngle(CAB),x)', 'PerpendicularBetweenLine(DB,CB)'], textCDL:['Equal(LengthOfLine(AB),y)', 'Equal(LengthOfLine(AC),12)', 'Equal(LengthOfLine(AD),LengthOfLine(BD))', 'Equal(MeasureOfAngle(CAB),x)', 'PerpendicularBetweenLine(DB,CB)', 'Square(ADBC)'].
|
74
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AN=10, BC=30, CN=5, AC is perpendicular to NC. Find the area of triangle ABC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AB,BC,CA)', 'Shape(AC,CN,NA)', 'Collinear(BCN)'], imgCDL:['Equal(LengthOfLine(AN),10)', 'Equal(LengthOfLine(BC),30)', 'Equal(LengthOfLine(CN),5)', 'PerpendicularBetweenLine(AC,NC)'], textCDL:['Equal(LengthOfLine(AN),10)', 'Equal(LengthOfLine(BC),30)', 'Equal(LengthOfLine(CN),5)', 'PerpendicularBetweenLine(AC,NC)'].
|
75
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, DE=6*x-12, FE=4*y, GD=6*y-42, GF=2*x+36, EDGF is a parallelogram. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(ED,DG,GF,FE)'], imgCDL:['Equal(LengthOfLine(DE),6*x-12)', 'Equal(LengthOfLine(FE),4*y)', 'Equal(LengthOfLine(GD),6*y-42)', 'Equal(LengthOfLine(GF),2*x+36)'], textCDL:['Equal(LengthOfLine(DE),6*x-12)', 'Equal(LengthOfLine(FE),4*y)', 'Equal(LengthOfLine(GD),6*y-42)', 'Equal(LengthOfLine(GF),2*x+36)', 'Parallelogram(EDGF)'].
|
78
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, BA=5, BC=12, DB=10, EB=x, O is the center of ⊙O. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(ODA,AB,BD)', 'Shape(OAE,EB,BA)', 'Shape(OEC,CB,BE)', 'Shape(OCD,DB,BC)', 'Collinear(ABC)', 'Collinear(EBD)', 'Cocircular(O,AECD)'], imgCDL:['Equal(LengthOfLine(BA),5)', 'Equal(LengthOfLine(BC),12)', 'Equal(LengthOfLine(DB),10)', 'Equal(LengthOfLine(EB),x)'], textCDL:['Equal(LengthOfLine(BA),5)', 'Equal(LengthOfLine(BC),12)', 'Equal(LengthOfLine(DB),10)', 'Equal(LengthOfLine(EB),x)', 'IsCentreOfCircle(O,O)'].
|
79
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, BC=x, BQ=6, QC=8. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AD,DB,BC,CA)', 'Shape(DQ,QB,BD)', 'Collinear(ADQ)', 'Collinear(QBC)'], imgCDL:['Equal(LengthOfLine(BC),x)', 'Equal(LengthOfLine(BQ),6)', 'Equal(LengthOfLine(QC),8)'], textCDL:['Equal(LengthOfLine(BC),x)', 'Equal(LengthOfLine(BQ),6)', 'Equal(LengthOfLine(QC),8)'].
|
80
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DEF=5*x°, ∠FDE=5*x°, ∠GFE=9*x+7°. Find ∠GFE. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(GF,FE)', 'Shape(FD,DE,EF)', 'Collinear(GFD)'], imgCDL:['Equal(MeasureOfAngle(DEF),5*x)', 'Equal(MeasureOfAngle(FDE),5*x)', 'Equal(MeasureOfAngle(GFE),9*x+7)'], textCDL:['Equal(MeasureOfAngle(DEF),5*x)', 'Equal(MeasureOfAngle(FDE),5*x)', 'Equal(MeasureOfAngle(GFE),9*x+7)'].
|
81
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, JL=y+4/5, LC=2*y-11/5, MI=12-3*x, TM=10-2*x, TM=MI, JT∥LM, LM∥CI. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(JL,LM,MT,TJ)', 'Shape(LC,CI,IM,ML)', 'Collinear(JLC)', 'Collinear(TMI)'], imgCDL:['Equal(LengthOfLine(JL),y+4/5)', 'Equal(LengthOfLine(LC),2*y-11/5)', 'Equal(LengthOfLine(MI),12-3*x)', 'Equal(LengthOfLine(TM),10-2*x)', 'Equal(LengthOfLine(TM),LengthOfLine(MI))', 'ParallelBetweenLine(JT,LM)', 'ParallelBetweenLine(LM,CI)'], textCDL:['Equal(LengthOfLine(JL),y+4/5)', 'Equal(LengthOfLine(LC),2*y-11/5)', 'Equal(LengthOfLine(MI),12-3*x)', 'Equal(LengthOfLine(TM),10-2*x)', 'Equal(LengthOfLine(TM),LengthOfLine(MI))', 'ParallelBetweenLine(JT,LM)', 'ParallelBetweenLine(LM,CI)'].
|
83
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=32, AD=DC, BC=2*x-3, EF=12, EH=HG, FG=x-5, ∠BCD=∠FGH, ∠DAB=∠HEF. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(EF,FH,HE)', 'Shape(HF,FG,GH)', 'Shape(AB,BD,DA)', 'Shape(DB,BC,CD)', 'Collinear(EHG)', 'Collinear(ADC)'], imgCDL:['Equal(LengthOfLine(AB),32)', 'Equal(LengthOfLine(AD),LengthOfLine(DC))', 'Equal(LengthOfLine(BC),2*x-3)', 'Equal(LengthOfLine(EF),12)', 'Equal(LengthOfLine(EH),LengthOfLine(HG))', 'Equal(LengthOfLine(FG),x-5)', 'Equal(MeasureOfAngle(BCD),MeasureOfAngle(FGH))', 'Equal(MeasureOfAngle(DAB),MeasureOfAngle(HEF))'], textCDL:['Equal(LengthOfLine(AB),32)', 'Equal(LengthOfLine(AD),LengthOfLine(DC))', 'Equal(LengthOfLine(BC),2*x-3)', 'Equal(LengthOfLine(EF),12)', 'Equal(LengthOfLine(EH),LengthOfLine(HG))', 'Equal(LengthOfLine(FG),x-5)', 'Equal(MeasureOfAngle(BCD),MeasureOfAngle(FGH))', 'Equal(MeasureOfAngle(DAB),MeasureOfAngle(HEF))'].
|
84
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABC=110°. Find the measure of ∠CBD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AB,BC)', 'Shape(CB,BD)', 'Collinear(ABD)'], imgCDL:['Equal(MeasureOfAngle(ABC),110)'], textCDL:['Equal(MeasureOfAngle(ABC),110)'].
|
85
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DGH=64°, BC∥DE, DF is parallel to GH. Find the measure of ∠JGD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AB,BC)', 'Shape(CB,BD)', 'Shape(BD,DE)', 'Shape(ED,DF)', 'Shape(FD,DG)', 'Shape(DG,GH)', 'Shape(HG,GI)', 'Shape(IG,GJ)', 'Shape(GJ,JK)', 'Shape(KJ,JL)', 'Shape(LJ,JB)', 'Shape(JB,BA)', 'Shape(BJ,JG,GD,DB)', 'Collinear(ABDF)', 'Collinear(LJGH)', 'Collinear(CBJK)', 'Collinear(EDGI)'], imgCDL:['Equal(MeasureOfAngle(DGH),64)', 'ParallelBetweenLine(BC,DE)', 'ParallelBetweenLine(DF,GH)'], textCDL:['Equal(MeasureOfAngle(DGH),64)', 'ParallelBetweenLine(BC,DE)', 'ParallelBetweenLine(DF,GH)'].
|
89
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, WX=a+12, WZ=4*a-15, XY=YZ, WY perpendicular bisects ZX. Find the length of line WX. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(WZ,ZY,YW)', 'Shape(WY,YX,XW)', 'Collinear(ZYX)'], imgCDL:['Equal(LengthOfLine(WX),a+12)', 'Equal(LengthOfLine(WZ),4*a-15)', 'Equal(LengthOfLine(XY),LengthOfLine(YZ))'], textCDL:['Equal(LengthOfLine(WX),a+12)', 'Equal(LengthOfLine(WZ),4*a-15)', 'Equal(LengthOfLine(XY),LengthOfLine(YZ))', 'IsPerpendicularBisectorOfLine(WY,ZX)'].
|
91
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DHB=38°, ∠FDA=52°, HB⊥DB. Find the measure of ∠HDF. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(CH,HI)', 'Shape(IH,HD)', 'Shape(HD,DF)', 'Shape(FD,DA)', 'Shape(AD,DB)', 'Shape(DB,BE)', 'Shape(EB,BG)', 'Shape(GB,BH)', 'Shape(BH,HC)', 'Shape(HB,BD,DH)', 'Collinear(CHDA)', 'Collinear(IHBE)', 'Collinear(GBDF)'], imgCDL:['Equal(MeasureOfAngle(DHB),38)', 'Equal(MeasureOfAngle(FDA),52)', 'PerpendicularBetweenLine(HB,DB)'], textCDL:['Equal(MeasureOfAngle(DHB),38)', 'Equal(MeasureOfAngle(FDA),52)', 'PerpendicularBetweenLine(HB,DB)'].
|
93
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠DBC=170°, the center of circle D is D. Find the measure of ∠CAB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(DCA,AC)', 'Shape(DC,CA,AD)', 'Shape(DA,AB,BD)', 'Shape(DAB,BA)', 'Shape(DB,DBC,CD)', 'Cocircular(D,CAB)'], imgCDL:['Equal(MeasureOfArc(DBC),170)'], textCDL:['Equal(MeasureOfArc(DBC),170)', 'IsCentreOfCircle(D,D)'].
|
94
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠PNO=56°, ∠BMN=70°, B is the center of ⊙B. Find the measure of ⌒BOP. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BPM,MP)', 'Shape(BMN,NP,PM)', 'Shape(PN,NO,BOP)', 'Shape(BNO,ON)', 'Cocircular(B,PMNO)'], imgCDL:['Equal(MeasureOfAngle(PNO),56)', 'Equal(MeasureOfArc(BMN),70)'], textCDL:['Equal(MeasureOfAngle(PNO),56)', 'Equal(MeasureOfArc(BMN),70)', 'IsCentreOfCircle(B,B)'].
|
95
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ACB=3*y+36°, ∠BDA=9*y-12°, ∠CBD=12*x+72°, ∠DAC=25*x+20°, quadrilateral BDAC is a parallelogram. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BD,DA,AC,CB)'], imgCDL:['Equal(MeasureOfAngle(ACB),3*y+36)', 'Equal(MeasureOfAngle(BDA),9*y-12)', 'Equal(MeasureOfAngle(CBD),12*x+72)', 'Equal(MeasureOfAngle(DAC),25*x+20)'], textCDL:['Equal(MeasureOfAngle(ACB),3*y+36)', 'Equal(MeasureOfAngle(BDA),9*y-12)', 'Equal(MeasureOfAngle(CBD),12*x+72)', 'Equal(MeasureOfAngle(DAC),25*x+20)', 'Parallelogram(BDAC)'].
|
96
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AD=11, BC=25, CA and CD are one pair of adjacent sides of the kite BACD. Find Area(BACD). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BA,AO,OB)', 'Shape(BO,OD,DB)', 'Shape(AC,CO,OA)', 'Shape(OC,CD,DO)', 'Collinear(COB)', 'Collinear(AOD)'], imgCDL:['Equal(LengthOfLine(AD),11)', 'Equal(LengthOfLine(BC),25)'], textCDL:['Equal(LengthOfLine(AD),11)', 'Equal(LengthOfLine(BC),25)', 'Kite(BACD)'].
|
97
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠CBD=55°, ∠FBG=35°, the center of ⊙B is B. Find the measure of arc BFA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BCA,AB,BC)', 'Shape(BAG,GB,BA)', 'Shape(BGF,FB,BG)', 'Shape(BFD,DB,BF)', 'Shape(BDC,CB,BD)', 'Collinear(ABD)', 'Collinear(CBG)', 'Cocircular(B,CAGFD)'], imgCDL:['Equal(MeasureOfAngle(CBD),55)', 'Equal(MeasureOfAngle(FBG),35)'], textCDL:['Equal(MeasureOfAngle(CBD),55)', 'Equal(MeasureOfAngle(FBG),35)', 'IsCentreOfCircle(B,B)'].
|
98
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, PQ=25*sqrt(3), RQ=25, PQ is perpendicular to RQ. Find ∠QRP. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(PQ,QR,RP)'], imgCDL:['Equal(LengthOfLine(PQ),25*sqrt(3))', 'Equal(LengthOfLine(RQ),25)', 'PerpendicularBetweenLine(PQ,RQ)'], textCDL:['Equal(LengthOfLine(PQ),25*sqrt(3))', 'Equal(LengthOfLine(RQ),25)', 'PerpendicularBetweenLine(PQ,RQ)'].
|
99
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=z, AN=x, AY=5, YB=14, YN=y, BA is perpendicular to YA, YN is perpendicular to AN. Find the value of y. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AY,YN,NA)', 'Shape(AN,NB,BA)', 'Collinear(YNB)'], imgCDL:['Equal(LengthOfLine(AB),z)', 'Equal(LengthOfLine(AN),x)', 'Equal(LengthOfLine(AY),5)', 'Equal(LengthOfLine(YB),14)', 'Equal(LengthOfLine(YN),y)', 'PerpendicularBetweenLine(BA,YA)', 'PerpendicularBetweenLine(YN,AN)'], textCDL:['Equal(LengthOfLine(AB),z)', 'Equal(LengthOfLine(AN),x)', 'Equal(LengthOfLine(AY),5)', 'Equal(LengthOfLine(YB),14)', 'Equal(LengthOfLine(YN),y)', 'PerpendicularBetweenLine(BA,YA)', 'PerpendicularBetweenLine(YN,AN)'].
|
100
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=c, CA=b, CB=a, ∠ABC=60°, ∠CAB=30°, b=18, BC is perpendicular to AC. Find the value of c. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BC,CA,AB)'], imgCDL:['Equal(LengthOfLine(AB),c)', 'Equal(LengthOfLine(CA),b)', 'Equal(LengthOfLine(CB),a)', 'Equal(MeasureOfAngle(ABC),60)', 'Equal(MeasureOfAngle(CAB),30)', 'PerpendicularBetweenLine(BC,AC)'], textCDL:['Equal(LengthOfLine(AB),c)', 'Equal(LengthOfLine(CA),b)', 'Equal(LengthOfLine(CB),a)', 'Equal(MeasureOfAngle(ABC),60)', 'Equal(MeasureOfAngle(CAB),30)', 'Equal(b,18)', 'PerpendicularBetweenLine(BC,AC)'].
|
103
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=x, AC=y, BC=6, ∠BAC=30°, AC⊥BC. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(CB,BA,AC)'], imgCDL:['Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(AC),y)', 'Equal(LengthOfLine(BC),6)', 'Equal(MeasureOfAngle(BAC),30)', 'PerpendicularBetweenLine(AC,BC)'], textCDL:['Equal(LengthOfLine(AB),x)', 'Equal(LengthOfLine(AC),y)', 'Equal(LengthOfLine(BC),6)', 'Equal(MeasureOfAngle(BAC),30)', 'PerpendicularBetweenLine(AC,BC)'].
|
104
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AD=15, PF=6, the centroid of triangle ACE is P. Find the length of line PC. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AB,BP,PA)', 'Shape(PB,BC,CP)', 'Shape(PC,CD,DP)', 'Shape(AP,PF,FA)', 'Shape(PD,DE,EP)', 'Shape(FP,PE,EF)', 'Collinear(ABC)', 'Collinear(CDE)', 'Collinear(EFA)', 'Collinear(BPE)', 'Collinear(CPF)', 'Collinear(APD)'], imgCDL:['Equal(LengthOfLine(AD),15)', 'Equal(LengthOfLine(PF),6)'], textCDL:['Equal(LengthOfLine(AD),15)', 'Equal(LengthOfLine(PF),6)', 'IsCentroidOfTriangle(P,ACE)'].
|
105
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, Area(ABCD) is 846, the area of quadrilateral EFGH is 376, CB=x, FG=24, quadrilateral ABCD is similar to quadrilateral EFGH. Find The ratio of similar quadrilaterals ABCD and EFGH. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(DA,AB,BC,CD)', 'Shape(HE,EF,FG,GH)'], imgCDL:['Equal(LengthOfLine(CB),x)', 'Equal(LengthOfLine(FG),24)'], textCDL:['Equal(AreaOfQuadrilateral(ABCD),846)', 'Equal(AreaOfQuadrilateral(EFGH),376)', 'Equal(LengthOfLine(CB),x)', 'Equal(LengthOfLine(FG),24)', 'SimilarBetweenQuadrilateral(ABCD,EFGH)'].
|
106
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=15*x+9, AC=7*x, BC=11*x+5, Perimeter(△CBA) is 320. Find CB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(CB,BA,AC)'], imgCDL:['Equal(LengthOfLine(AB),15*x+9)', 'Equal(LengthOfLine(AC),7*x)', 'Equal(LengthOfLine(BC),11*x+5)'], textCDL:['Equal(LengthOfLine(AB),15*x+9)', 'Equal(LengthOfLine(AC),7*x)', 'Equal(LengthOfLine(BC),11*x+5)', 'Equal(PerimeterOfTriangle(CBA),320)'].
|
107
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠PRQ=115°, R is the center of circle R, NR is perpendicular to PR. Find ⌒RMQ. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(RPN,NR,RP)', 'Shape(RNM,MR,RN)', 'Shape(RMQ,QR,RM)', 'Shape(RQP,PR,RQ)', 'Collinear(PRM)', 'Cocircular(R,PNMQ)'], imgCDL:['Equal(MeasureOfAngle(PRQ),115)', 'PerpendicularBetweenLine(NR,PR)'], textCDL:['Equal(MeasureOfAngle(PRQ),115)', 'IsCentreOfCircle(R,R)', 'PerpendicularBetweenLine(NR,PR)'].
|
108
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, BO=15, BO=CA, CE=7, CO=13, CO=BA, OE⊥AE. Find the perimeter of quadrilateral OCAB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(OC,CE,EO)', 'Shape(OE,EA,AB,BO)', 'Collinear(CEA)'], imgCDL:['Equal(LengthOfLine(BO),15)', 'Equal(LengthOfLine(BO),LengthOfLine(CA))', 'Equal(LengthOfLine(CE),7)', 'Equal(LengthOfLine(CO),13)', 'Equal(LengthOfLine(CO),LengthOfLine(BA))', 'PerpendicularBetweenLine(OE,AE)'], textCDL:['Equal(LengthOfLine(BO),15)', 'Equal(LengthOfLine(BO),LengthOfLine(CA))', 'Equal(LengthOfLine(CE),7)', 'Equal(LengthOfLine(CO),13)', 'Equal(LengthOfLine(CO),LengthOfLine(BA))', 'PerpendicularBetweenLine(OE,AE)'].
|
110
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, RQ=5, VS=11, S bisects segment RT, V bisects segment QU, quadrilateral QUTR is a trapezoid. Find the length of line UT. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(QV,VS,SR,RQ)', 'Shape(VU,UT,TS,SV)', 'Collinear(QVU)', 'Collinear(RST)'], imgCDL:['Equal(LengthOfLine(RQ),5)', 'Equal(LengthOfLine(VS),11)'], textCDL:['Equal(LengthOfLine(RQ),5)', 'Equal(LengthOfLine(VS),11)', 'IsMidpointOfLine(S,RT)', 'IsMidpointOfLine(V,QU)', 'Trapezoid(QUTR)'].
|
112
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, FK=3*x-1, JK=6*y-2, KG=4*y+3, KH=2*x+3, FJHG is a ▱. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(FJ,JK,KF)', 'Shape(KJ,JH,HK)', 'Shape(KH,HG,GK)', 'Shape(FK,KG,GF)', 'Collinear(FKH)', 'Collinear(JKG)'], imgCDL:['Equal(LengthOfLine(FK),3*x-1)', 'Equal(LengthOfLine(JK),6*y-2)', 'Equal(LengthOfLine(KG),4*y+3)', 'Equal(LengthOfLine(KH),2*x+3)'], textCDL:['Equal(LengthOfLine(FK),3*x-1)', 'Equal(LengthOfLine(JK),6*y-2)', 'Equal(LengthOfLine(KG),4*y+3)', 'Equal(LengthOfLine(KH),2*x+3)', 'Parallelogram(FJHG)'].
|
113
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=5, BC=x, ∠ABC=60°, ∠CAB=30°. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BC,CA,AB)'], imgCDL:['Equal(LengthOfLine(AC),5)', 'Equal(LengthOfLine(BC),x)', 'Equal(MeasureOfAngle(ABC),60)', 'Equal(MeasureOfAngle(CAB),30)'], textCDL:['Equal(LengthOfLine(AC),5)', 'Equal(LengthOfLine(BC),x)', 'Equal(MeasureOfAngle(ABC),60)', 'Equal(MeasureOfAngle(CAB),30)'].
|
114
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠FOE=118°, ∠LDA=104°, OD∥FI. Find ∠OFI. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(LD,DA)', 'Shape(AD,DI)', 'Shape(DI,IB)', 'Shape(BI,IC)', 'Shape(CI,IF)', 'Shape(IF,FJ)', 'Shape(JF,FK)', 'Shape(KF,FO)', 'Shape(FO,OE)', 'Shape(EO,OH)', 'Shape(HO,OD)', 'Shape(ID,DL)', 'Shape(DO,OF,FI,ID)', 'Collinear(LDIC)', 'Collinear(HOFJ)', 'Collinear(ADOE)', 'Collinear(BIFK)'], imgCDL:['Equal(MeasureOfAngle(FOE),118)', 'Equal(MeasureOfAngle(LDA),104)', 'ParallelBetweenLine(OD,FI)'], textCDL:['Equal(MeasureOfAngle(FOE),118)', 'Equal(MeasureOfAngle(LDA),104)', 'ParallelBetweenLine(OD,FI)'].
|
115
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠GOI=3*y+1°, ∠HBI=3*x+11°, ∠OIE=4*x-5°, GE is parallel to OI, IB is parallel to OH, OI∥HB. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(GO,OI,IE,EG)', 'Shape(OH,HB,BI,IO)', 'Collinear(GOH)', 'Collinear(BIE)'], imgCDL:['Equal(MeasureOfAngle(GOI),3*y+1)', 'Equal(MeasureOfAngle(HBI),3*x+11)', 'Equal(MeasureOfAngle(OIE),4*x-5)', 'ParallelBetweenLine(GE,OI)', 'ParallelBetweenLine(IB,OH)', 'ParallelBetweenLine(OI,HB)'], textCDL:['Equal(MeasureOfAngle(GOI),3*y+1)', 'Equal(MeasureOfAngle(HBI),3*x+11)', 'Equal(MeasureOfAngle(OIE),4*x-5)', 'ParallelBetweenLine(GE,OI)', 'ParallelBetweenLine(IB,OH)', 'ParallelBetweenLine(OI,HB)'].
|
116
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=5*sqrt(26), AD=25, CB=sqrt(26), CD=5, DB=1, ∠BCD=y°, ∠DCA=x°, AD⊥CD, BC⊥AC. Find the value of Cos(CAD). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(CA,AD,DC)', 'Shape(CD,DB,BC)', 'Collinear(ADB)'], imgCDL:['Equal(LengthOfLine(AC),5*sqrt(26))', 'Equal(LengthOfLine(AD),25)', 'Equal(LengthOfLine(CB),sqrt(26))', 'Equal(LengthOfLine(CD),5)', 'Equal(LengthOfLine(DB),1)', 'Equal(MeasureOfAngle(BCD),y)', 'Equal(MeasureOfAngle(DCA),x)', 'PerpendicularBetweenLine(AD,CD)', 'PerpendicularBetweenLine(BC,AC)'], textCDL:['Equal(LengthOfLine(AC),5*sqrt(26))', 'Equal(LengthOfLine(AD),25)', 'Equal(LengthOfLine(CB),sqrt(26))', 'Equal(LengthOfLine(CD),5)', 'Equal(LengthOfLine(DB),1)', 'Equal(MeasureOfAngle(BCD),y)', 'Equal(MeasureOfAngle(DCA),x)', 'PerpendicularBetweenLine(AD,CD)', 'PerpendicularBetweenLine(BC,AC)'].
|
117
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, the center of ⊙A is A, DF is the tangent to circle A. Find ∠AFD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AF,AFB,BA)', 'Shape(AB,ABF,FA)', 'Shape(AF,FD)', 'Collinear(FAB)', 'Cocircular(A,FB)'], imgCDL:[], textCDL:['IsCentreOfCircle(A,A)', 'IsTangentOfCircle(DF,A)'].
|
118
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, WX=9*x, WY=6*x+3, WY=YX, XW=WY, YX=4*x+5. Find the measure of ∠XWY. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(XW,WY,YX)'], imgCDL:['Equal(LengthOfLine(WX),9*x)', 'Equal(LengthOfLine(WY),6*x+3)', 'Equal(LengthOfLine(WY),LengthOfLine(YX))', 'Equal(LengthOfLine(XW),LengthOfLine(WY))', 'Equal(LengthOfLine(YX),4*x+5)'], textCDL:['Equal(LengthOfLine(WX),9*x)', 'Equal(LengthOfLine(WY),6*x+3)', 'Equal(LengthOfLine(WY),LengthOfLine(YX))', 'Equal(LengthOfLine(XW),LengthOfLine(WY))', 'Equal(LengthOfLine(YX),4*x+5)'].
|
119
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, CB=4*w-7, CD=11, ED=3*z+10, RS=2*w+13, RU=12, UT=z+16, ∠CBE=2*x+9°, ∠EDC=2*y-31°, ∠STU=y+11°, ∠URS=49°, quadrilateral BEDC is mirror congruent to quadrilateral RSTU. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BE,ED,DC,CB)', 'Shape(UR,RS,ST,TU)'], imgCDL:['Equal(LengthOfLine(CB),4*w-7)', 'Equal(LengthOfLine(CD),11)', 'Equal(LengthOfLine(ED),3*z+10)', 'Equal(LengthOfLine(RS),2*w+13)', 'Equal(LengthOfLine(RU),12)', 'Equal(LengthOfLine(UT),z+16)', 'Equal(MeasureOfAngle(CBE),2*x+9)', 'Equal(MeasureOfAngle(EDC),2*y-31)', 'Equal(MeasureOfAngle(STU),y+11)', 'Equal(MeasureOfAngle(URS),49)'], textCDL:['Equal(LengthOfLine(CB),4*w-7)', 'Equal(LengthOfLine(CD),11)', 'Equal(LengthOfLine(ED),3*z+10)', 'Equal(LengthOfLine(RS),2*w+13)', 'Equal(LengthOfLine(RU),12)', 'Equal(LengthOfLine(UT),z+16)', 'Equal(MeasureOfAngle(CBE),2*x+9)', 'Equal(MeasureOfAngle(EDC),2*y-31)', 'Equal(MeasureOfAngle(STU),y+11)', 'Equal(MeasureOfAngle(URS),49)', 'MirrorCongruentBetweenQuadrilateral(BEDC,RSTU)'].
|
122
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, WT=3, WX⊥YX, XY is perpendicular to ZY, YZ⊥WZ, ZW⊥XW, XYZW is a square. Find the length of line XY. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(XY,YT,TX)', 'Shape(TY,YZ,ZT)', 'Shape(TZ,ZW,WT)', 'Shape(XT,TW,WX)', 'Collinear(XTZ)', 'Collinear(WTY)'], imgCDL:['Equal(LengthOfLine(WT),3)', 'PerpendicularBetweenLine(WX,YX)', 'PerpendicularBetweenLine(XY,ZY)', 'PerpendicularBetweenLine(YZ,WZ)', 'PerpendicularBetweenLine(ZW,XW)'], textCDL:['Equal(LengthOfLine(WT),3)', 'PerpendicularBetweenLine(WX,YX)', 'PerpendicularBetweenLine(XY,ZY)', 'PerpendicularBetweenLine(YZ,WZ)', 'PerpendicularBetweenLine(ZW,XW)', 'Square(XYZW)'].
|
124
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ABH=3*p-10°, ∠CDB=6*r+5°, ∠JAB=4*p+15°, AJ is parallel to BH, CI∥AL. Find the value of r. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(LA,AJ)', 'Shape(JA,AB)', 'Shape(AB,BH)', 'Shape(HB,BE)', 'Shape(EB,BD)', 'Shape(BD,DK)', 'Shape(KD,DF)', 'Shape(FD,DC)', 'Shape(DC,CG)', 'Shape(GC,CI)', 'Shape(IC,CA)', 'Shape(CA,AL)', 'Shape(AC,CD,DB,BA)', 'Collinear(LABE)', 'Collinear(ICDK)', 'Collinear(JACG)', 'Collinear(HBDF)'], imgCDL:['Equal(MeasureOfAngle(ABH),3*p-10)', 'Equal(MeasureOfAngle(CDB),6*r+5)', 'Equal(MeasureOfAngle(JAB),4*p+15)', 'ParallelBetweenLine(AJ,BH)', 'ParallelBetweenLine(CI,AL)'], textCDL:['Equal(MeasureOfAngle(ABH),3*p-10)', 'Equal(MeasureOfAngle(CDB),6*r+5)', 'Equal(MeasureOfAngle(JAB),4*p+15)', 'ParallelBetweenLine(AJ,BH)', 'ParallelBetweenLine(CI,AL)'].
|
125
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, DA=3, DC=CB, DC⊥AC. Find the length of line AB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AD,DC,CA)', 'Shape(AC,CB,BA)', 'Collinear(DCB)'], imgCDL:['Equal(LengthOfLine(DA),3)', 'Equal(LengthOfLine(DC),LengthOfLine(CB))', 'PerpendicularBetweenLine(DC,AC)'], textCDL:['Equal(LengthOfLine(DA),3)', 'Equal(LengthOfLine(DC),LengthOfLine(CB))', 'PerpendicularBetweenLine(DC,AC)'].
|
126
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠ADK=96°, ∠HGJ=42°, GA∥HD. Find ∠GHD. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(KD,DL)', 'Shape(LD,DH)', 'Shape(DH,HI)', 'Shape(IH,HC)', 'Shape(CH,HG)', 'Shape(HG,GJ)', 'Shape(JG,GF)', 'Shape(FG,GA)', 'Shape(GA,AM)', 'Shape(MA,AF)', 'Shape(FA,AD)', 'Shape(AD,DK)', 'Shape(DA,AG,GH,HD)', 'Collinear(KDHC)', 'Collinear(EAGJ)', 'Collinear(LDAM)', 'Collinear(IHGF)'], imgCDL:['Equal(MeasureOfAngle(ADK),96)', 'Equal(MeasureOfAngle(HGJ),42)', 'ParallelBetweenLine(GA,HD)'], textCDL:['Equal(MeasureOfAngle(ADK),96)', 'Equal(MeasureOfAngle(HGJ),42)', 'ParallelBetweenLine(GA,HD)'].
|
127
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, ∠GKM=62°. Find the measure of ∠BKG. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(GK,KM)', 'Shape(BK,KG)', 'Collinear(MKB)'], imgCDL:['Equal(MeasureOfAngle(GKM),62)'], textCDL:['Equal(MeasureOfAngle(GKM),62)'].
|
128
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, SR=5, TR=3, TS=4, RT is perpendicular to ST. Find the value of Cos(TSR). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(TS,SR,RT)'], imgCDL:['Equal(LengthOfLine(SR),5)', 'Equal(LengthOfLine(TR),3)', 'Equal(LengthOfLine(TS),4)', 'PerpendicularBetweenLine(RT,ST)'], textCDL:['Equal(LengthOfLine(SR),5)', 'Equal(LengthOfLine(TR),3)', 'Equal(LengthOfLine(TS),4)', 'PerpendicularBetweenLine(RT,ST)'].
|
129
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AJ=2*x+3, BJ=5*x, JC=8*y-36, JD=4*y, AD and CB are opposite sides of the parallelogram ACBD. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(AC,CJ,JA)', 'Shape(JC,CB,BJ)', 'Shape(JB,BD,DJ)', 'Shape(AJ,JD,DA)', 'Collinear(AJB)', 'Collinear(CJD)'], imgCDL:['Equal(LengthOfLine(AJ),2*x+3)', 'Equal(LengthOfLine(BJ),5*x)', 'Equal(LengthOfLine(JC),8*y-36)', 'Equal(LengthOfLine(JD),4*y)'], textCDL:['Equal(LengthOfLine(AJ),2*x+3)', 'Equal(LengthOfLine(BJ),5*x)', 'Equal(LengthOfLine(JC),8*y-36)', 'Equal(LengthOfLine(JD),4*y)', 'Parallelogram(ACBD)'].
|
132
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AB=36, AD=22, ∠BCE=30°, BCDA is a parallelogram, CE is perpendicular to BE. Find the perimeter of quadrilateral BCDA. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BC,CE,EB)', 'Shape(BE,ED,DA,AB)', 'Collinear(CED)'], imgCDL:['Equal(LengthOfLine(AB),36)', 'Equal(LengthOfLine(AD),22)', 'Equal(MeasureOfAngle(BCE),30)', 'PerpendicularBetweenLine(CE,BE)'], textCDL:['Equal(LengthOfLine(AB),36)', 'Equal(LengthOfLine(AD),22)', 'Equal(MeasureOfAngle(BCE),30)', 'Parallelogram(BCDA)', 'PerpendicularBetweenLine(CE,BE)'].
|
133
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, CB=44, EA=19, ∠ACE=30°, BDAC is a parallelogram, DE⊥CE. Find Area(BDAC). Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BD,DE,EC,CB)', 'Shape(CE,EA,AC)', 'Collinear(DEA)'], imgCDL:['Equal(LengthOfLine(CB),44)', 'Equal(LengthOfLine(EA),19)', 'Equal(MeasureOfAngle(ACE),30)', 'PerpendicularBetweenLine(DE,CE)'], textCDL:['Equal(LengthOfLine(CB),44)', 'Equal(LengthOfLine(EA),19)', 'Equal(MeasureOfAngle(ACE),30)', 'Parallelogram(BDAC)', 'PerpendicularBetweenLine(DE,CE)'].
|
134
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=25, AD=21, EB=20, CADB is a ▱, DE is perpendicular to BE. Find the area of CADB. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(CA,AD,DB,BC)', 'Shape(BD,DE,EB)', 'Collinear(ADE)'], imgCDL:['Equal(LengthOfLine(AC),25)', 'Equal(LengthOfLine(AD),21)', 'Equal(LengthOfLine(EB),20)', 'PerpendicularBetweenLine(DE,BE)'], textCDL:['Equal(LengthOfLine(AC),25)', 'Equal(LengthOfLine(AD),21)', 'Equal(LengthOfLine(EB),20)', 'Parallelogram(CADB)', 'PerpendicularBetweenLine(DE,BE)'].
|
135
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, AC=b, BA=c, BC=a, ∠ABC=60°, ∠CAB=30°, b=3, BC is perpendicular to AC. Find the value of c. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(BC,CA,AB)'], imgCDL:['Equal(LengthOfLine(AC),b)', 'Equal(LengthOfLine(BA),c)', 'Equal(LengthOfLine(BC),a)', 'Equal(MeasureOfAngle(ABC),60)', 'Equal(MeasureOfAngle(CAB),30)', 'PerpendicularBetweenLine(BC,AC)'], textCDL:['Equal(LengthOfLine(AC),b)', 'Equal(LengthOfLine(BA),c)', 'Equal(LengthOfLine(BC),a)', 'Equal(MeasureOfAngle(ABC),60)', 'Equal(MeasureOfAngle(CAB),30)', 'Equal(b,3)', 'PerpendicularBetweenLine(BC,AC)'].
|
136
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, JK=33, LK=x, ∠KLJ=45°, JK⊥LK. Find the value of x. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(JK,KL,LJ)'], imgCDL:['Equal(LengthOfLine(JK),33)', 'Equal(LengthOfLine(LK),x)', 'Equal(MeasureOfAngle(KLJ),45)', 'PerpendicularBetweenLine(JK,LK)'], textCDL:['Equal(LengthOfLine(JK),33)', 'Equal(LengthOfLine(LK),x)', 'Equal(MeasureOfAngle(KLJ),45)', 'PerpendicularBetweenLine(JK,LK)'].
|
139
|
|
<image>The Caption of this geometric diagram is:As shown in the diagram, RS=3*x-5, RT=2*x+7, RT=RS, ST=22. Prove that triangleRST is an isosceles triangle. Please provide the consCDL and imgCDL based on this given geometric diagram and provide the textCDL based on its caption.
|
consCDL:['Shape(RS,ST,TR)'], imgCDL:['Equal(LengthOfLine(RS),3*x-5)', 'Equal(LengthOfLine(RT),2*x+7)', 'Equal(LengthOfLine(RT),LengthOfLine(RS))', 'Equal(LengthOfLine(ST),22)'], textCDL:['Equal(LengthOfLine(RS),3*x-5)', 'Equal(LengthOfLine(RT),2*x+7)', 'Equal(LengthOfLine(RT),LengthOfLine(RS))', 'Equal(LengthOfLine(ST),22)'].
|
142
|
End of preview. Expand
in Data Studio
README.md exists but content is empty.
- Downloads last month
- 4