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

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) No,it is not correct to say that $\triangle PQD \sim \triangle RPD$ in general.
In $\triangle PQD$ and $\triangle RPD$:
$1$. $\angle PDQ = \angle PDR = 90^{\circ}$ (Given that $PD \perp QR$)
$2$. $PD = PD$ (Common side)
For two triangles to be similar,we need either $AA$,$SAS$,or $SSS$ similarity criteria. Here,we only have one angle and one side equal. We do not have information about the equality of other angles or the proportionality of other sides.
Therefore,$\triangle PQD$ is not necessarily similar to $\triangle RPD$ unless $\triangle PQR$ is a specific type of triangle (e.g.,if $\angle P = 90^{\circ}$ and $PD$ is the altitude to the hypotenuse,then $\triangle PQD \sim \triangle RPD$ by $AA$ similarity).

Explore More

Similar Questions

In $\Delta ABC$,the bisector of $\angle A$ intersects $\overline{BC}$ at $D$. If $AB = 12$,$BD = 9$ and $BC = 21$,find $AC$.

In $\Delta XYZ$,the bisector of $\angle Y$ intersects $\overline{XZ}$ at $M$. Then,which of the following holds true?

In $\Delta ABC$,$m\angle B = 90^{\circ}$ and $\overline{BM}$ is a median. If $AC = 20$,then $BM = \ldots$

In $\Delta ABC$,$\overline{AB} \cong \overline{AC}$ and $\overline{AD}$ is a median. If $BC = 12$ and $AD = 8$,find $AB$.

In $\Delta ABC$,$A-P-B$,$A-Q-C$ and $\overline{PQ} \parallel \overline{BC}$. Then,$\ldots \ldots \ldots$ holds good.

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo