id
int64 1
32
| split
stringclasses 1
value | statement
stringlengths 98
98
| jgex
stringlengths 67
67
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|---|---|---|---|
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
|
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