Start

Axiom 2 :If equals are added to equals the wholes are equals
Axiom 3: if equals are subtracted from equals the remainders are equals

Equals1 = 8.5 (slider from 1 to 10, step 0.1)
Equals2 = 3 (slider from 0 to 3, step 3)
A = (0, 0)
B = (0, 1)
C: (Equals1, 1)
E = (0, -1)
F: (Equals1, -1)
G = (0, 2)
H: (Equals1, 2)
I = (0, -2)
J: (Equals1, -2)
K: (Equals1 + Equals2, 1)
L: (Equals1 + Equals2, -1)
M: (Equals1 + Equals2, 2)
N: (Equals1 + Equals2, -2)
u = Vector(B, A)
v = Vector(G, B)
w = Vector(B, C)
a = Vector(G, H)
c = Vector(H, M)
e = Vector(C, K)
f = Vector(A, E)
g = Vector(E, I)
h = Vector(I, N)
i = Vector(E, L)
X: (Equals1 + Equals2, 0)
z = Vector(M, X)
b = Vector(N, X)
distanceGM = Distance(G, M)
TextGM: "\overline{" + (Name[G]) + (Name[M]) + "} \, = \, " + distanceGM
distanceBK = Distance(B, K)
TextBK: "\overline{" + (Name[B]) + (Name[K]) + "} \, = \, " + distanceBK
distanceEL = Distance(E, L)
TextEL: "\overline{" + (Name[E]) + (Name[L]) + "} \, = \, " + distanceEL
distanceIN = Distance(I, N)
TextIN: "\overline{" + (Name[I]) + (Name[N]) + "} \, = \, " + distanceIN
text1: "GH=BC=EF=IJ=" + Equals1 + "    and    HM=CK=FL=JN=" + Equals2 + ""
text2: "GH+HM=" + Equals1 + "+" + Equals2 + "=" + (Equals1 + Equals2) + "=GM

BC+CK=" + Equals1 + " + " + Equals2 + "= " + (Equals1 + Equals2) + "=BK

EF+FL=" + Equals1 + "+" + Equals2 + "=" + (Equals1 + Equals2) + "=EL

IJ+JN=" + Equals1 + "+" + Equals2 + "=" + (Equals1 + Equals2) + "=IN

.'. GM=BK=EL=IN=" + (Equals1 + Equals2) + ""