Ipoteza:
ABC-triunghi, DE||AB, D ∈ AC, E ∈ BC.
Concluzia:
AD/AC = BE/BC
Demonstrația:
[tex]\it DE||AB,\ cu\ D\in AC,\ E\in BC\ \stackrel{T.Thales}{\Longrightarrow}\ \dfrac{CD}{AD}=\dfrac{CE}{BE} \Longrightarrow\\ \\ \\ \Longrightarrow \dfrac{AD}{CD}=\dfrac{BE}{CE}\ \stackrel{derivare}{\Longrightarrow}\ \dfrac{AD}{CD+AD}=\dfrac{BE}{CE+BE} \Longrightarrow \dfrac{AD}{AC}=\dfrac{BE}{BC}\ \ \ [q.e.d.][/tex]
