Two line segments PQ and RS intersect at X in such a way that XP = XR. If $\angle PSX$ = $\angle RQX$, then one must have

Two line segments PQ and RS intersect at X in such a way that XP = XR. If $\angle PSX$ = $\angle RQX$, then one must have
1). PR = QS
2). PS =RQ
3). $\angle XSQ$ = $\angle XRP$
4). ar($\triangle PXR$) = ar($\triangle QXS$)

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