To use the SSS (Side-Side-Side) congruence theorem to state that triangles ΔOPQ and ΔRST are congruent, you need to have all three sides of one triangle equal to the three corresponding sides of the other triangle.
From the options given:
- \( QO \cong TR \)
- \( PQ \cong RT \)
- \( OQ \cong RS \)
- \( OP \cong RT \)
Out of these, only options 1, 2, and 3 provide comparisons between the sides of both triangles.
The additional necessary information needed would be to have either:
- The side \( OP \) compared to \( RS \) (i.e., \( OP \cong RS \)), or
- The side \( PQ \) compared to \( ST \).
In other words, you need to know one more side from triangle ΔOPQ that is equal to the corresponding side from triangle ΔRST in order to use the SSS congruence theorem. Among the options provided, none directly provide that needed information.
If you take the comparison between the sides of both triangles, an equal match would help confirm congruence. Thus, we need to know:
- An additional piece of information, such as if \( OP \cong RS \), to apply the SSS theorem and conclude \( ΔOPQ \cong ΔRST \).
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