$E$ and $F$ are points on the sides $PQ$ and $PR$ respectively of a $\Delta PQR$. For the following case,state whether $EF || QR$: $PE = 3.9 \ cm, EQ = 3 \ cm, PF = 3.6 \ cm$ and $FR = 2.4 \ cm$.

(N/A) According to the Converse of Thales Theorem (Basic Proportionality Theorem),$EF || QR$ if and only if $\frac{PE}{EQ} = \frac{PF}{FR}$.
Given values are:
$PE = 3.9 \ cm$
$EQ = 3 \ cm$
$PF = 3.6 \ cm$
$FR = 2.4 \ cm$
Calculating the ratios:
$\frac{PE}{EQ} = \frac{3.9}{3} = 1.3$
$\frac{PF}{FR} = \frac{3.6}{2.4} = 1.5$
Since $\frac{PE}{EQ} \neq \frac{PF}{FR}$ $(1.3 \neq 1.5)$,the condition for $EF$ being parallel to $QR$ is not satisfied.
Therefore,$EF$ is not parallel to $QR$.