r00
a = free a; b = free b; c = free c; d = on_tline d c a b; e = free e; f = on_tline f e c d ? para a b e f
r01
o = free o; a = free a; b = eqdistance b o o a; c = eqdistance c o o b; d = eqdistance d o o c ? cyclic a b c d
r02
p = free p; q = free q; a = free a; b = free b; c = free c; d = on_aline0 d p q a b p q c ? para a b c d
r03
a = free a; b = free b; p = free p; q = on_circum q a b p ? eqangle p a p b q a q b
r04
a = free a; b = free b; q = free q; p = eqangle3 p a b q a b ? cyclic a b p q
r05
a = free a; b = free b; c = free c; p = on_circum p a b c; r = on_circum r a b c; q = on_circum q a b c, on_aline q r p b c a ? cong a b p q
r06
a = free a; b = free b; c = free c; e = midpoint e a b; f = midpoint f a c ? para e f b c
r07
a = free a; b = free b; c = free c; d = on_pline d c a b; o = on_line o a c, on_line o b d ? eqratio o a o c o b o d; eqratio o a c a o b b d; eqratio o c a c o d b d
r08
a = free a; b = free b; c = free c; d = on_tline d c a b; e = free e; f = free f; g = free g; h = on_tline h g e f ? eqangle a b e f c d g h
r09
c = free c; d = free d; p = free p; q = free q; a = free a; b = free b; m = free m; n = on_aline0 n c d a b p q m; e = free e; f = free f; r = free r; u = on_aline0 u c d e f p q r ? eqangle a b e f m n r u
r10
a = free a; b = free b; c = free c; d = free d; m = free m; n = free n; p = free p; q = eqratio q a b c d m n p; e = free e; f = free f; r = free r; u = eqratio u c d e f p q r ? eqratio a b e f m n r u
r11
a = free a; b = free b; c = free c; d = eqratio6 d b c a b a c, on_line d b c ? eqangle a b a d a d a c
r12
a = free a; b = free b; d = free d; c = on_line c b d, on_aline c a d d a b ? eqratio d b d c a b a c
r13
o = free o; a = free a; b = eqdistance b o o a ? eqangle o a a b a b o b
r14
a = free a; b = free b; o = iso_triangle_vertex_angle o a b ? cong o a o b
r15
a = free a; b = free b; c = free c; o = circle o a b c; x = on_tline x a a o ? eqangle a x a b c a c b
r16
a = free a; b = free b; c = free c; o = circle o a b c; x = on_aline x a b a c b ? perp o a a x
r17
a = free a; b = free b; c = free c; o = circle o a b c; m = midpoint m b c ? eqangle a b a c o b o m
r18
a = free a; b = free b; c = free c; o = circle o a b c; m = on_line m b c, on_aline m o b c a b ? midp m b c
r19
a = free a; b = free b; c = on_tline c b b a; m = midpoint m a c ? cong a m b m
r20
o a b c = test_r20 o a b c ? perp a b b c
r21
a = free a; b = free b; c = free c; d = on_pline d c a b, on_circum d a b c ? eqangle a d c d c d c b
r22
a = free a; b = free b; m = midpoint m a b; o = on_tline o m a b ? cong o a o b
r23
a = free a; p = free p; q = free q; b = eqdistance b p a p, eqdistance b q a q ? perp a b p q
r24
a = free a; b = free b; p = iso_triangle_vertex p a b; q = iso_triangle_vertex q a b, on_circum q a b p ? perp p a a q
r25
a b c d m = test_r25 a b c d m ? para a c b d
r26
a = free a; b = free b; c = free c; d = on_pline d b a c, on_pline d a b c; m = midpoint m a b ? midp m c d
r27
o = free o; a = free a; b = free b; c = on_line c a o; d = eqratio d o a a c o b b, on_line d o b ? para a b c d
r28
a = free a; b = free b; c = on_pline0 c a b a ? coll a b c
r29
a = free a; b = free b; c = free c; d = free d; m = midpoint m a b; n = midpoint n c d ? eqratio m a a b n c c d
r30
p = free p; q = free q; u = free u; v = on_tline v u p q; a = free a; b = free b; c = free c; d = on_aline0 d p q a b u v c ? perp a b c d
r31
p = free p; q = free q; u = free u; v = eqdistance v u p q; a = free a; b = free b; c = free c; d = eqratio d p q a b u v c ? cong a b c d
r32
a b c = triangle a b c; p = free p; q = eqdistance q p a b; r = eqdistance r p a c, eqdistance r q c b ? contri a b c p q r
r33
a = free a; b = free b; c = free c; q = free q; p = eqdistance p q b a; r = eqdistance r q b c, on_aline r q p c b a ? contri a b c p q r
r34
a = free a; b = free b; c = free c; q = free q; r = free r; p = on_aline p q r a b c, on_aline p r q a c b ? simtri a b c p q r
r35
a = free a; b = free b; c = free c; q = free q; r = free r; p = on_aline p q r c b a, on_aline p r q b c a ? simtrir a b c p q r
r36
a = free a; b = free b; p = free p; q = eqdistance q p a b; r = free r; c = on_aline c b a r q p, eqangle3 c a b r p q ? contri a b c p q r
r37
a = free a; b = free b; p = free p; q = eqdistance q p a b; r = free r; c = on_aline c b a p q r, eqangle3 c a b r q p ? contrir a b c p q r
r38
a = free a; b = free b; c = free c; q = free q; r = free r; p = eqratio p b c b a q r q, eqratio p c b c a r q r ? simtri a b c p q r
r39
a = free a; b = free b; c = free c; p = free p; q = free q; r = eqratio r b a b c q p q, on_aline r q p c b a ? simtri a b c p q r
r40
a = free a; b = free b; c = free c; p = free p; q = eqdistance q p a b; r = eqratio r b a b c q p q, eqratio6 r p q c a c b ? contri a b c p q r
r41
a = free a; b = free b; c = free c; d = on_pline d c a b; n = on_line n b c; m = eqratio6 m a d n b n c, on_line m a d ? para m n a b
r42
a = free a; b = free b; c = free c; d = on_pline d c a b; m = on_line m a d; n = on_line n b c, on_pline n m a b ? eqratio m a m d n b n c
r43
a b c = triangle a b c; d = on_tline d c a b, on_tline d b a c ? perp a d b c
r44
a b = segment a b; c = on_line c a b; p q = segment p q; r = on_line r p q; x = on_line x a q, on_line x p b; y = on_line y a r, on_line y p c; z = on_line z b r, on_line z c q ? coll x y z
r45
a b c = triangle a b c; p = on_circum p a b c; l = on_line l a c, on_tline l p a c; m = on_line m b c, on_tline m p b c; n = on_line n a b, on_tline n p a b ? coll l m n
r46
a b c = triangle a b c; x = angle_bisector x b a c, angle_bisector x a b c ? eqangle c b c x c x c a
r47
a b c = triangle a b c; m = midpoint m a b; n = midpoint n b c; p = midpoint p c a; x = on_tline x m a b, on_tline x n b c ? perp x p c a
r48
a b c = triangle a b c; m = midpoint m a b; n = midpoint n b c; p = midpoint p c a; x = on_line x m c, on_line x n a ? coll x p b
r49
a b c = triangle a b c; o = circle o a b c; d = on_circum d a b c ? cong o a o d
r50
a = free a; b = free b; c = free c; d = on_circum d a b c; o = on_bline o a b, on_bline o c d ? cong o a o c
r51
a b = segment a b; m = midpoint m a b ? rconst m a a b 1/2
r52
a b c = triangle a b c; p q = segment p q; r = simtri r a b c p q ? eqangle b a b c q p q r; eqangle a b a c p q p r; eqangle a c b c p r q r; eqratio b a b c q p q r; eqratio b c a c q r p r
r53
a b c = triangle a b c; p q = segment p q; r = simtrir r a b c p q ? eqangle b a b c q r q p; eqangle a b a c p r p q; eqangle a c b c q r p r; eqratio b a b c q p q r; eqratio b c a c q r p r
r54
a b = segment a b; m = on_line m a b, on_bline m a b ? midp m a b
r55
a b = segment a b; m = midpoint m a b ? cong m a m b
r56
a b = segment a b; m = midpoint m a b ? coll m a b
r58
a = free a; b = free b; c = free c; p = on_circum p a b c; q = on_circum q b c p, eqdistance q p a b; r = on_circum r c p q ? sameclock c a b r p q; sameside c a b r p q; eqangle c a c b r p r q
r59
a = free a; b = free b; c = free c; p = on_circum p a b c; q = on_circum q b c p, eqdistance q p a b; r = on_circum r c p q ? sameclock c b a r p q; nsameside c b a r p q; eqangle c a c b r p r q
r60
a b c = triangle a b c; p q = segment p q; r = eqratio r b a b c q p q, eqratio6 r p q c a c b ? sameclock a b c p q r; simtri a b c p q r
r61
a b c = triangle a b c; p q = segment p q; r = eqratio r b a b c q p q, on_aline0 r b a b c q p q ? sameclock a b c p r q; simtrir a b c p q r
r62
a b c = triangle a b c; p q = segment p q; r = eqratio r b a b c q p q, on_aline0 r b a b c q p q ? sameclock a b c p q r; simtri a b c p q r
r63
a b c = triangle a b c; p q = segment p q; r = eqratio r b a b c q p q, on_aline0 r b c b a q p q ? sameclock a b c p r q; simtrir a b c p q r
r64
a b c = triangle a b c; p = free p; q = eqdistance q p a b; r = eqdistance r q b c, eqdistance r p a c ? sameclock a b c p q r; contri a b c p q r
r65
a b c = triangle a b c; p = free p; q = eqdistance q p a b; r = eqdistance r q b c, eqdistance r p a c ? sameclock a b c p r q; contrir a b c p q r
r66
a b c = triangle a b c; p = free p; q = eqdistance q p a b; r = eqdistance r q b c, on_aline0 r b a b c q p q ? sameclock a b c p q r;  contri a b c p q r
r67
a b c = triangle a b c; p = free p; q = eqdistance q p a b; r = eqdistance r q b c, on_aline0 r b c b a q p q ? sameclock a b c p r q;  contrir a b c p q r
r68
a b c = triangle a b c; p = free p; q = eqdistance q p a b; r = eqratio r b a b c q p q, eqratio6 r p q c a c b ? sameclock a b c p q r; contri a b c p q r
r69
a b c = triangle a b c; p = free p; q = eqdistance q p a b; r = eqratio r b a b c q p q, eqratio6 r p q c a c b ? sameclock a b c p r q; contrir a b c p q r
r70
a b = segment a b; c = on_line c a b; l = free l; m = on_line m a l; n = on_line n l b, on_line n m c; k = on_line k a n, on_line k b m; d = on_line d a b, on_line d k l ? eqratio a c a d b c b d
r71
a b = segment a b; c = on_line c a b; d e = segment d e; f = on_line f d e, eqratio f a b a c d e d ? eqratio a b b c d e e f
r72
a = free a; b = free b; c = free c; o = circle o a b c ? cong o a o b; cong o b o c
r73
o a = segment o a; b = eqdistance b o o a; c = eqdistance c o o b ? circle o a b c
r74
a b c = triangle a b c; d = on_bline d a b, angle_bisector d a c b ? cyclic a b c d
r75
a b = segment a b; c = on_line c b a; d e = segment d e; f = on_line f d e, eqratio f a b a c d e d ? eqratio a b b c d e e f
r76
a b = segment a b; c = on_tline c a a b; m = on_bline m a b, on_line m b c ? midp m b c
r77
a b c = triangle a b c; p = free p; q r = contri q r a b c p ? simtri a b c p q r; cong a b p q
r78
a b c = triangle a b c; p = free p; q r = contrir q r a b c p ? simtrir a b c p q r; cong a b p q
r79
a b = segment a b; c = free c; d = eqdistance d c a b; x y = segment x y ? eqratio a b x y c d x y
r80
p b = segment p b; a = free a; q = on_circum q a p b, eqdistance q p a b ? sameclock a b p b p q; eqangle p a p b p b q b
r81
p b = segment p b; a = free a; q = on_circum q a p b, eqdistance q p a b ? sameclock a b p b q p; eqangle p a p b q b p b
r82
a b = segment a b; c = on_line c a b ? para a b b c; para a b a c
r83
c a b = between c a b ? lequation 1/1 a c 1/1 c b -1/1 a b 0/1


r85
a b = segment a b; c = free c; d = on_tline d c a b ? lequation 1/1 a c * a c 1/1 b d * b d -1/1 a d * a d -1/1 b c * b c 0




r88
a b c = triangle a b c; o = circle o a b c ? aequation 1/1 A B B C 1/1 C A A O 90o
r89
a b c = triangle a b c; m = midpoint m a b ? lequation 2/1 A M * A M -2/1 B C * B C -2/1 A C * A C 1/1 A B * A B 0
r90
a b = segment a b; c = free c; d = on_pline d c a b, on_pline d a b c ? lequation 2/1 A B * A B 2/1 B C * B C -1/1 A C * A C -1/1 B D * B D 0
r91
a b = segment a b; c = free a; d = on_pline d a b c, eqdistance d c a b ? eqangle c a c b b c b d
r92
a b = segment a b; o = midpoint o a b; c = on_circle c o a; d = on_circum d a b c, eqdistance d c a b ? coll o c d