In quadrilateral $PQRS$, $PQ = PS$ and $PR$ bisccts $\angle P$. Show that $\triangle P R Q \cong \triangle PRS$.
What can you say about $QR$ and $SR$?
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Given :

In quadrilateral $PQRS$, $PQ =  PS$ and $PR$ bisccts $\angle P$. 

To do :

We have to show that,  $\triangle P R Q \cong \triangle PRS$.

Solution :

This implies,

$∠SPR = ∠QPR$

In Triangles $PSR$ and $PQR$,

$PQ = PS$  (Given)

$∠SPR = ∠QPR$

$PR = PR$  (Common side)

Therefore, by SAS congruence,

 $\triangle P R Q \cong \triangle PRS$

This implies,

$QR = SR$  (CPCT).

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Updated on: 10-Oct-2022

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