In the given figure,$PS = QR$ and $PR = QS$. Prove that $(1) \angle PSQ = \angle QRP$ and $(2) \angle SPQ = \angle RQP$.
(N/A) In $\Delta SPQ$ and $\Delta RQP$:
$PS = QR$ (Given)
$QS = PR$ (Given)
$PQ = QP$ (Common side)
Therefore,by $SSS$ congruence criterion,$\Delta SPQ \cong \Delta RQP$.
Since the triangles are congruent,their corresponding parts are equal $(CPCT)$.
Thus,$(1) \angle PSQ = \angle QRP$ and $(2) \angle SPQ = \angle RQP$.
$PS = QR$ (Given)
$QS = PR$ (Given)
$PQ = QP$ (Common side)
Therefore,by $SSS$ congruence criterion,$\Delta SPQ \cong \Delta RQP$.
Since the triangles are congruent,their corresponding parts are equal $(CPCT)$.
Thus,$(1) \angle PSQ = \angle QRP$ and $(2) \angle SPQ = \angle RQP$.
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