                                                          BASIC PROPORTIONAL THEOREM :
If a straight line drawn parallel to a side of a triangle, then it divides the other two sides proportionaly

a = 8 (slider from 1 to 12, step 1)
A = (0.9832111982488299, 2.267937229034934)
B = Point(Circle[A, abs(a)])
b = Segment(A, B)
C = (5.237419146469044, 8.640119949759608)
c = Segment(A, C)
d = Segment(B, C)
D = Point(c)
E = Point(d)
e = Segment(D, E)
distanceCE = Distance(C, E)
TextCE: Name[C] + (Name[E]) + " = " + distanceCE
distanceEB = Distance(E, B)
TextEB: Name[E] + (Name[B]) + " = " + distanceEB
distanceCD = Distance(C, D)
TextCD: Name[C] + (Name[D]) + " = " + distanceCD
distanceDA = Distance(D, A)
TextDA: Name[D] + (Name[A]) + " = " + distanceDA
T: Distance[C, E] / Distance[E, B]
T1: Distance[C, D] / Distance[D, A]
text2: "$\frac{CE}{EB}=\frac{" + (LaTeX[distanceCE]) + "} {" + (LaTeX[distanceEB]) + "}=" + (LaTeX[T]) + "$


$\frac{CD}{DA}=\frac{" + (LaTeX[distanceCD]) + "} {" + (LaTeX[distanceDA]) + "}=" + (LaTeX[T1]) + " $


$∴\frac{CE}{EB} = \frac{CD}{DA}"