Question

In the given quadrilateral, $QS$ is the bisector of $\angle S$ and $\angle Q$. $PS=5cm$ and $PQ=8cm$. Fin the measure of $SR$.

• A. 5 cm
• B. 8 cm
• C. 6 cm
• D. 13 cm

Answer 1

Answer: (A)

In figure,

$QS$ is the bisector of $\angle S$ and $\angle Q$.

$PS=5cm$

In $\Delta PSQ$ and $\Delta RSQ$

$\angle PSQ=\angle RSQ$ [Since, $QS$ is the bisector of $\angle S$.]

$SQ=SQ$ [Since, common side of $\Delta PSQ$ and $\Delta RSQ$]

$\angle PQS=\angle RQS$ [Since, $QS$ is the bisector of $\angle Q$.]

By, A.S.A congruence criterion,

$\Delta PSQ\cong \Delta RSQ$

By CPCT,

$SR=SP=PS=5cm$

Hence, Option A is correct.