In the given figure, $PS$ is the bisector of $\angle QPR$ of $∆PQR$. Prove that $\frac{QS}{SR}=\frac{PQ}{PR}$
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AcademicMathematicsNCERTClass 10

Given:

$PS$ is the bisector of $\angle QPR$ of $∆PQR$.

To do:

We have to prove that $\frac{QS}{SR}=\frac{PQ}{PR}$

Solution:

Draw $RT \| PS$,meeting $QP$ produced at $T$.
$PS \| RT$
This implies,
$\angle 2=\angle 3$             (Alternate angles)
$\angle 1=\angle 4$        (Corresponding angles)
$\angle 1 = \angle 2$       (AD is the bisector of $\angle A$)
Therefore,
$\angle 3 =\angle 4$
This implies,
 $PT=PR$
In $\triangle QRT$,
$\frac{QS}{SR}=\frac{PQ}{PT}$
$\frac{QS}{SR}=\frac{PQ}{PR}$

Hence proved.

raja
Updated on 10-Oct-2022 13:21:39

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