Question

State true or false:

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

• A. True
• B. False

Answer 1

The correct option is A True

Given: $△ABC\sim △PQR$
$\angle ABC=\angle PQR$ (Corresponding angles)
Now, $AD$ and $PM$ are altitudes of $△ABC$ and $△PQR$ respectively,
thus, in $△ABD$ and $△PQM$
$\angle ABD=\angle PQM$ (Since, $△ABC\sim △PQR$)
$\angle ADB=\angle PMQ$ (Each ${90}^{\circ }$)
$\angle BAD=\angle QPM$ (Third angle)
Thus, $△ABD\sim △PQM$ (AAA rule)
Hence, $\frac{AB}{PQ}=\frac{AD}{PM}$ (Corresponding sides)