Question

If M and N are the midpoints of PQ and PR in a triangle PQR then find the length of MN​ and QR=8cm

Answer 1

The length of $MN$ is $4\ cm$

Step-by-step explanation:

Given,

$M$ and $N$ are the midpoints of $PQ$ and $PR$ in a $\triangle PQR$ where $QR=8\ cm$

In figure,

∵$M$ and $N$ are the midpoints of $PQ$ and $PR$

∴$MN\parallel QR$

In $\triangle PQR\ and\ \triangle PMN$

• $\angle PMN=\angle PQR$ (∵ $MN\parallel QR$)

• $\angle PNM=\angle PRQ$ (∵ $MN\parallel QR$)

• $\angle P$ common.

$\triangle PQR$≅$\triangle PMN$

∴ $\frac{PM}{PQ}=\frac{MN}{QR}$

⇒$\frac{PM}{2PM}=\frac{MN}{8}$

⇒$\frac{1}{2}=\frac{MN}{8}$

⇒$2MN=8$

⇒$MN=4\ cm$

So, The length of $MN$ is $4\ cm$