Question

Question 10
D is a point on side QR of $\Delta PQR$ such that $PD\perp QR$. Will it be correct to say that $\Delta PQD\sim \Delta RPD$? Why?

Answer 1

Flase
In $\Delta PQDand\Delta RPD$
PD = PD [Common side]
$\angle PDQ=\angle PDR$ $\left[each{90}^{\circ }\right]$


Here, no other sides or angles are equal, so we can say that $\Delta PDQ$ is not similar to $\Delta RPD$
But, if $\angle P={90}^{\circ },then\angle DPQ=\angle RPD$ [ each equal to ${90}^{\circ }-\angle \theta$]
and by ASA similarity criterion, we can say that $\Delta PQD\sim \Delta RPD$.