Neka je
![ABCD](/media/m/9/c/e/9ce25711ba18d9663b73c3580de4bf5a.png)
paralelogram,
![E](/media/m/8/b/0/8b01e755d2253cb9a52f9e451d89ec11.png)
polovište stranice
![\overline{AB}](/media/m/a/1/a/a1a42310b1a849922197735f632d57ec.png)
,
![F](/media/m/3/e/8/3e8bad5df716d332365fca76f53c1743.png)
polovište stranice
![\overline{BC}](/media/m/8/8/1/8818caad7d36e134c54122cbf46f1cd9.png)
i
![P](/media/m/9/6/8/968d210d037e7e95372de185e8fb8759.png)
sjecište dužina
![\overline{EC}](/media/m/5/b/b/5bb4f62da6c45de0eaf91964064f3c64.png)
i
![\overline{FD}](/media/m/d/5/8/d581e3fd3815057766db5a52e8b3c88e.png)
. Dokaži da dužine
![\overline{AP}](/media/m/6/b/a/6ba025fd7238b82fe483707d613e3026.png)
,
![\overline{BP}](/media/m/9/3/2/9329c3f0d9d2c336788b3125529f9bea.png)
,
![\overline{CP}](/media/m/6/d/3/6d312290a4295a66b7eafae1f66d0eba.png)
i
![\overline{DP}](/media/m/d/2/a/d2a8b5fde0afc2ca6e0bee08e47cf57e.png)
dijele paralelogram na trokute čije se površine u nekom poretku odnose kao
![1:2:3:4](/media/m/8/e/7/8e7d97d5788755b844942b9e6dced226.png)
.
%V0
Neka je $ABCD$ paralelogram, $E$ polovište stranice $\overline{AB}$, $F$ polovište stranice $\overline{BC}$ i $P$ sjecište dužina $\overline{EC}$ i $\overline{FD}$. Dokaži da dužine $\overline{AP}$, $\overline{BP}$, $\overline{CP}$ i $\overline{DP}$ dijele paralelogram na trokute čije se površine u nekom poretku odnose kao $1:2:3:4$.