Thales of Miletus was an ancient Greek philosopher and mathematician considered one of the first philosophers in the Greek tradition. He used geometry to solve practical problems and is credited with Thales' theorem, which states that if two lines intersected by parallel lines form intercepts, the ratios of the corresponding line segments are equal. The document then provides an example problem applying Thales' theorem to find the length of line segment BE given the information provided.

1. Thales of
Miletus
Thales of Miletus ( c. 624
BC – c. 546 BC) was a
pre-Socratic Greek
philosopher from Miletus
in Asia Minor, and one of
the Seven Sages of
Greece. . Many regard
him as the first
philosopher in the Greek
tradition. In
mathematics, Thales
used geometry to solve
problems such as
calculating the height of
pyramids and the
distance of ships from
the shore.

2. Thales’ Theorem
The intercept theorem,
also known as Thales'
theorem , is an important
theorem in elementary
geometry about the
ratios of various line
segments that are
created if two
intersecting lines are
intercepted by a pair of
parallels. It is equivalent
to the theorem about
ratios in similar
triangles. Traditionally it
is attributed to Greek
mathematician Thales.

3. Thales’ Theorem
If a//d ,x=z ,
AC=4 and
ED=9
Find the
length of BE
and CD

4. Answer
A. A. x= 6
B. B. x=12
C. C. x=9
D. D. z=4