In the figure,$PQ > PR$ and $QS$ and $RS$ are the bisectors of $\angle Q$ and $\angle R$,respectively. Show that $SQ > SR$.

Vedclass pdf generator app on play store
Vedclass iOS app on app store
(N/A) Given: In $\triangle PQR$,$PQ > PR$ and $QS$,$RS$ are bisectors of $\angle Q$ and $\angle R$ respectively.
Since $PQ > PR$,the angle opposite to the longer side is greater. Therefore,$\angle R > \angle Q$.
Since $QS$ and $RS$ are bisectors of $\angle Q$ and $\angle R$ respectively,we have:
$\angle SQR = \frac{1}{2} \angle Q$
$\angle SRQ = \frac{1}{2} \angle R$
Since $\angle R > \angle Q$,it follows that $\frac{1}{2} \angle R > \frac{1}{2} \angle Q$.
Therefore,$\angle SRQ > \angle SQR$.
In $\triangle SQR$,since $\angle SRQ > \angle SQR$,the side opposite to the greater angle is longer. Thus,$SQ > SR$.

Explore More

Similar Questions

$\angle ABD$ and $\angle ACE$ are exterior angles of $\Delta ABC$. If $\angle ABD > \angle ACE$,then prove that $AC > AB$.

$D$ is a point on the side $BC$ of a $\triangle ABC$ such that $AD$ bisects $\angle BAC$. Then

In $\Delta ABC$,$\angle B = 90^{\circ}$,$BC = 8 \, \text{cm}$,and $AC = 17 \, \text{cm}$. $BE$ is a median of the triangle and $M$ is the midpoint of $BE$. Find the area of $\Delta BMC$ in $\text{cm}^2$.

In $\Delta XYZ$,$XY > XZ$ and $P$ is any point on the side $YZ$. Prove that $XY > XP$.

In $\Delta XYZ$,$XY = XZ$ and $\angle X = 80^{\circ}$,then $\angle Y = \ldots$ (in $^{\circ}$)

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