[tex]\it \begin{cases}\it AB||CD\\ \\ AC-secant\breve a\end{cases} \Rightarrow \hat A=\hat C\ (corespondente)\ \ \ \ \ \ (1)\\ \\ \\ \begin{cases}\it BC||DE\\ \\ CE-secant\breve a\end{cases} \Rightarrow \hat C=\hat E\ (corespondente)\ \ \ \ \ \ (2)\\ \\ \\ (1),\ (2) \Rightarrow \Delta ABC \sim \Delta CDE\ (cazul\ UU) \ \ \ \ \ \ (3)[/tex]
[tex]\it AE=4Ce \Rightarrow AC+CE=4CE|_{-CE} \Rightarrow AC=3CE\ \ \ \ \ \ (4)\\ \\ (3) \Rightarrow k=\dfrac{AC}{CE}=\dfrac{3CE}{CE}=3\ (raportul\ de\ asem\breve anare)[/tex]
[tex]\it \dfrac{\mathcal{P}_{ABC}}{\mathcal{P}_{CDE}}=k=3\\ \\ \\ \dfrac{\mathcal{A}_{ABC}}{\mathcal{A}_{CDE}}=k^2=3^2=9 \Rightarrow \dfrac{\mathcal{A}_{CDE}}{\mathcal{A}_{ABC}}=\dfrac{1}{9}[/tex]
