Basic Proportionality Theorem (BPT)
The Basic Proportionality Theorem (also known as Thales’ theorem) states that if a line is drawn parallel to one side of a triangle to intersect the other two sides, then it divides those two sides proportionally.
In the diagram above, if line DE is parallel to BC, then according to the Basic Proportionality Theorem:
\[
\frac{AD}{DB} = \frac{AE}{EC}
\]
This theorem is widely used in geometry to prove the similarity of triangles and to solve problems involving proportions.