$E$ and $F$ are points on the sides $PQ$ and $PR$ respectively of a $\triangle PQR$. For each of the following cases, state whether $EF \| QR$:
$PE = 4\ cm, QE = 4.5\ cm, PF = 8\ cm$ and $RF = 9\ cm$
Given:
$PE = 4\ cm, QE = 4.5\ cm, PF = 8\ cm$ and $RF = 9\ cm$
To do:
We have to find if $EF\parallel QR$.
Solution:
We know that,
If a line divides two sides of a triangle proportionally, then it is parallel to the third side.
$\frac{PE}{EQ}=\frac{4}{4.5}=\frac{8}{9}$
$\frac{PF}{FR}=\frac{8}{9}$
$\frac{PE}{EQ}=\frac{PF}{FR}$
Hence, by converse of proportionality theorem $EF$ is parallel to $QR$.
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