In order to state that triangles \( \Delta OPQ \) and \( \Delta RST \) are congruent by the SSS (Side-Side-Side) congruence theorem, you need to confirm that all three pairs of corresponding sides of the triangles are equal.
From the information provided, we have:
- \( QO = TR \)
- \( PQ = RT \)
- \( OQ = RS \)
However, it seems like there is a mistake or redundancy with \( OP = RT \). For SSS to hold, we need the values for all three sides of both triangles (OP, OQ, and PQ for triangle OPQ and RS, RT, and TR for triangle RST).
Here, it looks like what you actually need is the length of one more side. Specifically, the sides \( OP \) and \( RS \) need to be stated as equal. If you confirm that \( OP = RS \), it would allow you to use the SSS criterion to state that \( \Delta OPQ \cong \Delta RST \). Thus, the additional information needed is that \( OP = RS \).
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