What additional piece of information is needed in order to state that OPQ=RST by the SSS congruence theorem?

Question

OP=RT OQ=RS PQ=RT QO=TR.

Answer 1

To state that triangles OPQ and RST are congruent by the Side-Side-Side (SSS) congruence theorem, we need to ensure that all three pairs of corresponding sides are equal.

From the information provided, we have:

1. OP = RT (one pair of sides is equal)
2. OQ = RS (another pair of sides is equal)
3. PQ is given to be equal to RT

However, for SSS, we require three pairs of sides that match:

• OP = RT
• OQ = RS
• PQ = ST (assuming ST is the third side in triangle RST that corresponds to side PQ in triangle OPQ)

Thus, the additional piece of information needed is PQ = ST in order to conclude that triangles OPQ and RST are congruent by the SSS theorem.