$ \mathrm{D} $ is a point on side $ \mathrm{QR} $ of $ \triangle \mathrm{PQR} $ such that $ \mathrm{PD} \perp \mathrm{QR} $. Will it be correct to say that $ \triangle \mathrm{PQD} \sim \triangle \mathrm{RPD} $ ? Why?

Given:

\( \mathrm{D} \) is a point on side \( \mathrm{QR} \) of \( \triangle \mathrm{PQR} \) such that \( \mathrm{PD} \perp \mathrm{QR} \).

To do:

We have to find whether \( \triangle \mathrm{PQD} \sim \triangle \mathrm{RPD} \).

Solution:

In $\triangle PQD$ and $\triangle RPD$,

$PD = PD$           (Common side)

$\angle PDQ = \angle PDR=90^o$

Here,

No other sides or angles are equal, so we can say that $\triangle PQD$ is not similar to $\triangle RPD$.