Question

State true or false:

Triangle $ABC$ is similar to triangle $PQR$. If $AD$ and $PM$ are corresponding medians of the two triangles. Then,
$\frac{AB}{PQ}=\frac{AD}{PM}.$

• A. True
• B. False

Answer 1

The correct option is A True

Given: $△ABC\sim △PQR$
$\frac{AB}{PQ}=\frac{BC}{QR}=\frac{AC}{PR}$ (Corresponding sides)
or $\frac{AB}{PQ}=\frac{\frac{1}{2}BC}{\frac{1}{2}QR}$
$\angle ABC=\angle PQR$ (Corresponding angles)
Now, $AD$ and $PM$ are medians of $△ABC$ and $△PQR$ respectively,
Thus, in $△ABD$ and $△PQM$
$\angle ABD=\angle PQM$ (Since, $△ABC\sim △PQR$)
$\frac{AB}{PQ}=\frac{BD}{QM}$ ($AD$ and $PM$ are medians)
Thus, $△ABD\sim △PQM$ (SAS rule)
Hence, $\frac{AB}{PQ}=\frac{AD}{PM}$