\( \mathrm{D} \) 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 $\triangle RPD$.
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