id
int64 1
137
| split
stringclasses 1
value | statement
stringlengths 98
98
| jgex
stringlengths 67
67
|
|---|---|---|---|
1
|
train
|
Given segment $AC$, construct a square $ACEF$ with side $AC$. Prove that $AC\perp CE$ and $AC=CE$.
|
a c = segment a c;e f = square e f a c ? perp a c c e; cong a c c e
|
2
|
train
|
Given segment $AD$, construct a square $ADGH$ with side $AD$. Prove that $AD\perp DG$ and $AD=DG$.
|
a d = segment a d;g h = square g h a d ? perp a d d g; cong a d d g
|
3
|
train
|
Given segment $AE$, construct a square $AEIJ$ with side $AE$. Prove that $AE\perp EI$ and $AE=EI$.
|
a e = segment a e;i j = square i j a e ? perp a e e i; cong a e e i
|
4
|
train
|
Given segment $AF$, construct a square $AFKL$ with side $AF$. Prove that $AF\perp FK$ and $AF=FK$.
|
a f = segment a f;k l = square k l a f ? perp a f f k; cong a f f k
|
5
|
train
|
Given segment $AG$, construct a square $AGMN$ with side $AG$. Prove that $AG\perp GM$ and $AG=GM$.
|
a g = segment a g;m n = square m n a g ? perp a g g m; cong a g g m
|
6
|
train
|
Given segment $AH$, construct a square $AHOP$ with side $AH$. Prove that $AH\perp HO$ and $AH=HO$.
|
a h = segment a h;o p = square o p a h ? perp a h h o; cong a h h o
|
7
|
train
|
Given segment $AI$, construct a square $AIQR$ with side $AI$. Prove that $AI\perp IQ$ and $AI=IQ$.
|
a i = segment a i;q r = square q r a i ? perp a i i q; cong a i i q
|
8
|
train
|
Given segment $AJ$, construct a square $AJST$ with side $AJ$. Prove that $AJ\perp JS$ and $AJ=JS$.
|
a j = segment a j;s t = square s t a j ? perp a j j s; cong a j j s
|
9
|
train
|
Given segment $AK$, construct a square $AKUV$ with side $AK$. Prove that $AK\perp KU$ and $AK=KU$.
|
a k = segment a k;u v = square u v a k ? perp a k k u; cong a k k u
|
10
|
train
|
Given segment $AL$, construct a square $ALWX$ with side $AL$. Prove that $AL\perp LW$ and $AL=LW$.
|
a l = segment a l;w x = square w x a l ? perp a l l w; cong a l l w
|
11
|
train
|
Given segment $AM$, construct a square $AMYZ$ with side $AM$. Prove that $AM\perp MY$ and $AM=MY$.
|
a m = segment a m;y z = square y z a m ? perp a m m y; cong a m m y
|
12
|
train
|
Given segment $AN$, construct a square $ANPQ$ with side $AN$. Prove that $AN\perp NP$ and $AN=NP$.
|
a n = segment a n;p q = square p q a n ? perp a n n p; cong a n n p
|
13
|
train
|
Given segment $AO$, construct a square $AORS$ with side $AO$. Prove that $AO\perp OR$ and $AO=OR$.
|
a o = segment a o;r s = square r s a o ? perp a o o r; cong a o o r
|
14
|
train
|
Given segment $AP$, construct a square $APTU$ with side $AP$. Prove that $AP\perp PT$ and $AP=PT$.
|
a p = segment a p;t u = square t u a p ? perp a p p t; cong a p p t
|
15
|
train
|
Given segment $AQ$, construct a square $AQVW$ with side $AQ$. Prove that $AQ\perp QV$ and $AQ=QV$.
|
a q = segment a q;v w = square v w a q ? perp a q q v; cong a q q v
|
16
|
train
|
Given segment $AR$, construct a square $ARXY$ with side $AR$. Prove that $AR\perp RX$ and $AR=RX$.
|
a r = segment a r;x y = square x y a r ? perp a r r x; cong a r r x
|
17
|
train
|
Given segment $AS$, construct a square $ASBD$ with side $AS$. Prove that $AS\perp SB$ and $AS=SB$.
|
a s = segment a s;b d = square b d a s ? perp a s s b; cong a s s b
|
18
|
train
|
Given segment $AT$, construct a square $ATCE$ with side $AT$. Prove that $AT\perp TC$ and $AT=TC$.
|
a t = segment a t;c e = square c e a t ? perp a t t c; cong a t t c
|
19
|
train
|
Given segment $BC$, construct a square $BCFG$ with side $BC$. Prove that $BC\perp CF$ and $BC=CF$.
|
b c = segment b c;f g = square f g b c ? perp b c c f; cong b c c f
|
20
|
train
|
Given segment $BD$, construct a square $BDHI$ with side $BD$. Prove that $BD\perp DH$ and $BD=DH$.
|
b d = segment b d;h i = square h i b d ? perp b d d h; cong b d d h
|
21
|
train
|
Given segment $BE$, construct a square $BEJK$ with side $BE$. Prove that $BE\perp EJ$ and $BE=EJ$.
|
b e = segment b e;j k = square j k b e ? perp b e e j; cong b e e j
|
22
|
train
|
Given segment $BF$, construct a square $BFLM$ with side $BF$. Prove that $BF\perp FL$ and $BF=FL$.
|
b f = segment b f;l m = square l m b f ? perp b f f l; cong b f f l
|
23
|
train
|
Given segment $BG$, construct a square $BGNO$ with side $BG$. Prove that $BG\perp GN$ and $BG=GN$.
|
b g = segment b g;n o = square n o b g ? perp b g g n; cong b g g n
|
24
|
train
|
Given segment $BH$, construct a square $BHPQ$ with side $BH$. Prove that $BH\perp HP$ and $BH=HP$.
|
b h = segment b h;p q = square p q b h ? perp b h h p; cong b h h p
|
25
|
train
|
Given segment $BI$, construct a square $BIRS$ with side $BI$. Prove that $BI\perp IR$ and $BI=IR$.
|
b i = segment b i;r s = square r s b i ? perp b i i r; cong b i i r
|
26
|
train
|
Given segment $BJ$, construct a square $BJTU$ with side $BJ$. Prove that $BJ\perp JT$ and $BJ=JT$.
|
b j = segment b j;t u = square t u b j ? perp b j j t; cong b j j t
|
27
|
train
|
Given segment $BK$, construct a square $BKVW$ with side $BK$. Prove that $BK\perp KV$ and $BK=KV$.
|
b k = segment b k;v w = square v w b k ? perp b k k v; cong b k k v
|
28
|
train
|
Given segment $BL$, construct a square $BLXY$ with side $BL$. Prove that $BL\perp LX$ and $BL=LX$.
|
b l = segment b l;x y = square x y b l ? perp b l l x; cong b l l x
|
29
|
train
|
Given segment $BM$, construct a square $BMAD$ with side $BM$. Prove that $BM\perp MA$ and $BM=MA$.
|
b m = segment b m;a d = square a d b m ? perp b m m a; cong b m m a
|
30
|
train
|
Given segment $BN$, construct a square $BNEF$ with side $BN$. Prove that $BN\perp NE$ and $BN=NE$.
|
b n = segment b n;e f = square e f b n ? perp b n n e; cong b n n e
|
31
|
train
|
Given segment $BO$, construct a square $BOGH$ with side $BO$. Prove that $BO\perp OG$ and $BO=OG$.
|
b o = segment b o;g h = square g h b o ? perp b o o g; cong b o o g
|
32
|
train
|
Given segment $BP$, construct a square $BPIJ$ with side $BP$. Prove that $BP\perp PI$ and $BP=PI$.
|
b p = segment b p;i j = square i j b p ? perp b p p i; cong b p p i
|
70
|
train
|
Given segment $AU$, construct a square $AUVW$ with side $AU$. Prove that $AU\perp UV$ and $AU=UV$.
|
a u = segment a u;v w = square v w a u ? perp a u u v; cong a u u v
|
71
|
train
|
Given segment $AV$, construct a square $AVWX$ with side $AV$. Prove that $AV\perp VW$ and $AV=VW$.
|
a v = segment a v;w x = square w x a v ? perp a v v w; cong a v v w
|
72
|
train
|
Given segment $AW$, construct a square $AWXY$ with side $AW$. Prove that $AW\perp WX$ and $AW=WX$.
|
a w = segment a w;x y = square x y a w ? perp a w w x; cong a w w x
|
73
|
train
|
Given segment $AX$, construct a square $AXYZ$ with side $AX$. Prove that $AX\perp XY$ and $AX=XY$.
|
a x = segment a x;y z = square y z a x ? perp a x x y; cong a x x y
|
74
|
train
|
Given segment $AY$, construct a square $AYCD$ with side $AY$. Prove that $AY\perp YC$ and $AY=YC$.
|
a y = segment a y;c d = square c d a y ? perp a y y c; cong a y y c
|
75
|
train
|
Given segment $AZ$, construct a square $AZEF$ with side $AZ$. Prove that $AZ\perp ZE$ and $AZ=ZE$.
|
a z = segment a z;e f = square e f a z ? perp a z z e; cong a z z e
|
76
|
train
|
Given segment $BU$, construct a square $BUVW$ with side $BU$. Prove that $BU\perp UV$ and $BU=UV$.
|
b u = segment b u;v w = square v w b u ? perp b u u v; cong b u u v
|
77
|
train
|
Given segment $BV$, construct a square $BVWX$ with side $BV$. Prove that $BV\perp VW$ and $BV=VW$.
|
b v = segment b v;w x = square w x b v ? perp b v v w; cong b v v w
|
78
|
train
|
Given segment $BW$, construct a square $BWXY$ with side $BW$. Prove that $BW\perp WX$ and $BW=WX$.
|
b w = segment b w;x y = square x y b w ? perp b w w x; cong b w w x
|
79
|
train
|
Given segment $BX$, construct a square $BXYZ$ with side $BX$. Prove that $BX\perp XY$ and $BX=XY$.
|
b x = segment b x;y z = square y z b x ? perp b x x y; cong b x x y
|
80
|
train
|
Given segment $BY$, construct a square $BYCD$ with side $BY$. Prove that $BY\perp YC$ and $BY=YC$.
|
b y = segment b y;c d = square c d b y ? perp b y y c; cong b y y c
|
81
|
train
|
Given segment $BZ$, construct a square $BZEF$ with side $BZ$. Prove that $BZ\perp ZE$ and $BZ=ZE$.
|
b z = segment b z;e f = square e f b z ? perp b z z e; cong b z z e
|
82
|
train
|
Given segment $EF$, construct a square $EFGH$ with side $EF$. Prove that $EF\perp FG$ and $EF=FG$.
|
e f = segment e f;g h = square g h e f ? perp e f f g; cong e f f g
|
83
|
train
|
Given segment $EG$, construct a square $EGHI$ with side $EG$. Prove that $EG\perp GH$ and $EG=GH$.
|
e g = segment e g;h i = square h i e g ? perp e g g h; cong e g g h
|
84
|
train
|
Given segment $EH$, construct a square $EHJK$ with side $EH$. Prove that $EH\perp HJ$ and $EH=HJ$.
|
e h = segment e h;j k = square j k e h ? perp e h h j; cong e h h j
|
85
|
train
|
Given segment $IJ$, construct a square $IJKL$ with side $IJ$. Prove that $IJ\perp JK$ and $IJ=JK$.
|
i j = segment i j;k l = square k l i j ? perp i j j k; cong i j j k
|
86
|
train
|
Given segment $IK$, construct a square $IKLM$ with side $IK$. Prove that $IK\perp KL$ and $IK=KL$.
|
i k = segment i k;l m = square l m i k ? perp i k k l; cong i k k l
|
87
|
train
|
Given segment $MN$, construct a square $MNOP$ with side $MN$. Prove that $MN\perp NO$ and $MN=NO$.
|
m n = segment m n;o p = square o p m n ? perp m n n o; cong m n n o
|
88
|
train
|
Given segment $MO$, construct a square $MOPQ$ with side $MO$. Prove that $MO\perp OP$ and $MO=OP$.
|
m o = segment m o;p q = square p q m o ? perp m o o p; cong m o o p
|
89
|
train
|
Given segment $QR$, construct a square $QRST$ with side $QR$. Prove that $QR\perp RS$ and $QR=RS$.
|
q r = segment q r;s t = square s t q r ? perp q r r s; cong q r r s
|
90
|
train
|
Given segment $QS$, construct a square $QSTU$ with side $QS$. Prove that $QS\perp ST$ and $QS=ST$.
|
q s = segment q s;t u = square t u q s ? perp q s s t; cong q s s t
|
91
|
train
|
Given segment $UV$, construct a square $UVWX$ with side $UV$. Prove that $UV\perp VW$ and $UV=VW$.
|
u v = segment u v;w x = square w x u v ? perp u v v w; cong u v v w
|
92
|
train
|
Given segment $UW$, construct a square $UWXY$ with side $UW$. Prove that $UW\perp WX$ and $UW=WX$.
|
u w = segment u w;x y = square x y u w ? perp u w w x; cong u w w x
|
93
|
train
|
Given segment $YZ$, construct a square $YZCD$ with side $YZ$. Prove that $YZ\perp ZC$ and $YZ=ZC$.
|
y z = segment y z;c d = square c d y z ? perp y z z c; cong y z z c
|
94
|
train
|
Given segment $EI$, construct a square $EIJK$ with side $EI$. Prove that $EI\perp IJ$ and $EI=IJ$.
|
e i = segment e i;j k = square j k e i ? perp e i i j; cong e i i j
|
95
|
train
|
Given segment $EJ$, construct a square $EJKL$ with side $EJ$. Prove that $EJ\perp JK$ and $EJ=JK$.
|
e j = segment e j;k l = square k l e j ? perp e j j k; cong e j j k
|
96
|
train
|
Given segment $EK$, construct a square $EKLM$ with side $EK$. Prove that $EK\perp KL$ and $EK=KL$.
|
e k = segment e k;l m = square l m e k ? perp e k k l; cong e k k l
|
97
|
train
|
Given segment $EL$, construct a square $ELMN$ with side $EL$. Prove that $EL\perp LM$ and $EL=LM$.
|
e l = segment e l;m n = square m n e l ? perp e l l m; cong e l l m
|
98
|
train
|
Given segment $EM$, construct a square $EMNO$ with side $EM$. Prove that $EM\perp MN$ and $EM=MN$.
|
e m = segment e m;n o = square n o e m ? perp e m m n; cong e m m n
|
99
|
train
|
Given segment $EN$, construct a square $ENOP$ with side $EN$. Prove that $EN\perp NO$ and $EN=NO$.
|
e n = segment e n;o p = square o p e n ? perp e n n o; cong e n n o
|
100
|
train
|
Given segment $EO$, construct a square $EOPQ$ with side $EO$. Prove that $EO\perp OP$ and $EO=OP$.
|
e o = segment e o;p q = square p q e o ? perp e o o p; cong e o o p
|
101
|
train
|
Given segment $EP$, construct a square $EPQR$ with side $EP$. Prove that $EP\perp PQ$ and $EP=PQ$.
|
e p = segment e p;q r = square q r e p ? perp e p p q; cong e p p q
|
102
|
train
|
Given segment $EQ$, construct a square $EQRS$ with side $EQ$. Prove that $EQ\perp QR$ and $EQ=QR$.
|
e q = segment e q;r s = square r s e q ? perp e q q r; cong e q q r
|
103
|
train
|
Given segment $ER$, construct a square $ERST$ with side $ER$. Prove that $ER\perp RS$ and $ER=RS$.
|
e r = segment e r;s t = square s t e r ? perp e r r s; cong e r r s
|
104
|
train
|
Given segment $ES$, construct a square $ESTU$ with side $ES$. Prove that $ES\perp ST$ and $ES=ST$.
|
e s = segment e s;t u = square t u e s ? perp e s s t; cong e s s t
|
105
|
train
|
Given segment $ET$, construct a square $ETUV$ with side $ET$. Prove that $ET\perp TU$ and $ET=TU$.
|
e t = segment e t;u v = square u v e t ? perp e t t u; cong e t t u
|
106
|
train
|
Given segment $EU$, construct a square $EUVW$ with side $EU$. Prove that $EU\perp UV$ and $EU=UV$.
|
e u = segment e u;v w = square v w e u ? perp e u u v; cong e u u v
|
107
|
train
|
Given segment $EV$, construct a square $EVWX$ with side $EV$. Prove that $EV\perp VW$ and $EV=VW$.
|
e v = segment e v;w x = square w x e v ? perp e v v w; cong e v v w
|
108
|
train
|
Given segment $EW$, construct a square $EWXY$ with side $EW$. Prove that $EW\perp WX$ and $EW=WX$.
|
e w = segment e w;x y = square x y e w ? perp e w w x; cong e w w x
|
109
|
train
|
Given segment $EX$, construct a square $EXYZ$ with side $EX$. Prove that $EX\perp XY$ and $EX=XY$.
|
e x = segment e x;y z = square y z e x ? perp e x x y; cong e x x y
|
110
|
train
|
Given segment $EY$, construct a square $EYZA$ with side $EY$. Prove that $EY\perp YZ$ and $EY=YZ$.
|
e y = segment e y;z a = square z a e y ? perp e y y z; cong e y y z
|
111
|
train
|
Given segment $EZ$, construct a square $EZAB$ with side $EZ$. Prove that $EZ\perp ZA$ and $EZ=ZA$.
|
e z = segment e z;a b = square a b e z ? perp e z z a; cong e z z a
|
112
|
train
|
Given segment $FI$, construct a square $FIJK$ with side $FI$. Prove that $FI\perp IJ$ and $FI=IJ$.
|
f i = segment f i;j k = square j k f i ? perp f i i j; cong f i i j
|
113
|
train
|
Given segment $FJ$, construct a square $FJKL$ with side $FJ$. Prove that $FJ\perp JK$ and $FJ=JK$.
|
f j = segment f j;k l = square k l f j ? perp f j j k; cong f j j k
|
114
|
train
|
Given segment $FK$, construct a square $FKLM$ with side $FK$. Prove that $FK\perp KL$ and $FK=KL$.
|
f k = segment f k;l m = square l m f k ? perp f k k l; cong f k k l
|
115
|
train
|
Given segment $FL$, construct a square $FLMN$ with side $FL$. Prove that $FL\perp LM$ and $FL=LM$.
|
f l = segment f l;m n = square m n f l ? perp f l l m; cong f l l m
|
116
|
train
|
Given segment $FM$, construct a square $FMNO$ with side $FM$. Prove that $FM\perp MN$ and $FM=MN$.
|
f m = segment f m;n o = square n o f m ? perp f m m n; cong f m m n
|
117
|
train
|
Given segment $FN$, construct a square $FNOP$ with side $FN$. Prove that $FN\perp NO$ and $FN=NO$.
|
f n = segment f n;o p = square o p f n ? perp f n n o; cong f n n o
|
118
|
train
|
Given segment $FO$, construct a square $FOPQ$ with side $FO$. Prove that $FO\perp OP$ and $FO=OP$.
|
f o = segment f o;p q = square p q f o ? perp f o o p; cong f o o p
|
119
|
train
|
Given segment $FP$, construct a square $FPQR$ with side $FP$. Prove that $FP\perp PQ$ and $FP=PQ$.
|
f p = segment f p;q r = square q r f p ? perp f p p q; cong f p p q
|
120
|
train
|
Given segment $FQ$, construct a square $FQRS$ with side $FQ$. Prove that $FQ\perp QR$ and $FQ=QR$.
|
f q = segment f q;r s = square r s f q ? perp f q q r; cong f q q r
|
121
|
train
|
Given segment $FR$, construct a square $FRST$ with side $FR$. Prove that $FR\perp RS$ and $FR=RS$.
|
f r = segment f r;s t = square s t f r ? perp f r r s; cong f r r s
|
122
|
train
|
Given segment $FS$, construct a square $FSTU$ with side $FS$. Prove that $FS\perp ST$ and $FS=ST$.
|
f s = segment f s;t u = square t u f s ? perp f s s t; cong f s s t
|
123
|
train
|
Given segment $FT$, construct a square $FTUV$ with side $FT$. Prove that $FT\perp TU$ and $FT=TU$.
|
f t = segment f t;u v = square u v f t ? perp f t t u; cong f t t u
|
124
|
train
|
Given segment $FU$, construct a square $FUVW$ with side $FU$. Prove that $FU\perp UV$ and $FU=UV$.
|
f u = segment f u;v w = square v w f u ? perp f u u v; cong f u u v
|
125
|
train
|
Given segment $FV$, construct a square $FVWX$ with side $FV$. Prove that $FV\perp VW$ and $FV=VW$.
|
f v = segment f v;w x = square w x f v ? perp f v v w; cong f v v w
|
126
|
train
|
Given segment $FW$, construct a square $FWXY$ with side $FW$. Prove that $FW\perp WX$ and $FW=WX$.
|
f w = segment f w;x y = square x y f w ? perp f w w x; cong f w w x
|
127
|
train
|
Given segment $FX$, construct a square $FXYZ$ with side $FX$. Prove that $FX\perp XY$ and $FX=XY$.
|
f x = segment f x;y z = square y z f x ? perp f x x y; cong f x x y
|
128
|
train
|
Given segment $FY$, construct a square $FYZA$ with side $FY$. Prove that $FY\perp YZ$ and $FY=YZ$.
|
f y = segment f y;z a = square z a f y ? perp f y y z; cong f y y z
|
129
|
train
|
Given segment $FZ$, construct a square $FZAB$ with side $FZ$. Prove that $FZ\perp ZA$ and $FZ=ZA$.
|
f z = segment f z;a b = square a b f z ? perp f z z a; cong f z z a
|
130
|
train
|
Given segment $GI$, construct a square $GIJK$ with side $GI$. Prove that $GI\perp IJ$ and $GI=IJ$.
|
g i = segment g i;j k = square j k g i ? perp g i i j; cong g i i j
|
131
|
train
|
Given segment $GJ$, construct a square $GJKL$ with side $GJ$. Prove that $GJ\perp JK$ and $GJ=JK$.
|
g j = segment g j;k l = square k l g j ? perp g j j k; cong g j j k
|
132
|
train
|
Given segment $GK$, construct a square $GKLM$ with side $GK$. Prove that $GK\perp KL$ and $GK=KL$.
|
g k = segment g k;l m = square l m g k ? perp g k k l; cong g k k l
|
133
|
train
|
Given segment $GL$, construct a square $GLMN$ with side $GL$. Prove that $GL\perp LM$ and $GL=LM$.
|
g l = segment g l;m n = square m n g l ? perp g l l m; cong g l l m
|
134
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train
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Given segment $GM$, construct a square $GMNO$ with side $GM$. Prove that $GM\perp MN$ and $GM=MN$.
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g m = segment g m;n o = square n o g m ? perp g m m n; cong g m m n
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135
|
train
|
Given segment $GN$, construct a square $GNOP$ with side $GN$. Prove that $GN\perp NO$ and $GN=NO$.
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g n = segment g n;o p = square o p g n ? perp g n n o; cong g n n o
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136
|
train
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Given segment $GO$, construct a square $GOPQ$ with side $GO$. Prove that $GO\perp OP$ and $GO=OP$.
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g o = segment g o;p q = square p q g o ? perp g o o p; cong g o o p
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137
|
train
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Given segment $GP$, construct a square $GPQR$ with side $GP$. Prove that $GP\perp PQ$ and $GP=PQ$.
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g p = segment g p;q r = square q r g p ? perp g p p q; cong g p p q
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