M and N are points on the sides PQ and PR respectively of a $\triangle PQR$. For each of the following cases, state whether $MN \parallel QR$:
$PM = 4\ cm$, $QM = 4.5\ cm, PN = 4\ cm, NR = 4.5\ cm$

Given:

$PM=4\ cm, QM=4.5\ cm, PN=4\ cm$ and $NR=4.5\ cm$. 

To do:

We have to find if $MN\parallel QR$.

Solution:

We know that,

If a line divides two sides of a triangle proportionally, then it is parallel to the third side.

Therefore,

$\frac{PM}{QM}=\frac{4}{4.5}=\frac{4\times2}{4.5\times2}=\frac{8}{9}$

$\frac{PN}{NR}=\frac{4}{4.5}=\frac{4\times2}{4.5\times2}=\frac{8}{9}$

$\frac{PM}{QM}=\frac{PN}{NR}$

Hence, by converse of proportionality theorem $MN$ is parallel to $QR$.

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Updated on: 10-Oct-2022

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