6 of 156 of 15 Items Question Use the image to answer the question. What additional piece of information is needed in order to state that △OPQ≅△RST by the SSS Congruence Theorem? (1 point) Responses QO¯¯¯¯¯¯¯¯≅TR¯¯¯¯¯¯¯ line segment cap q cap o is congruent to line segment cap t cap r OQ¯¯¯¯¯¯¯¯≅RS¯¯¯¯¯¯¯ line segment cap o cap q is congruent to line segment cap r cap s OP¯¯¯¯¯¯¯¯≅RT¯¯¯¯¯¯¯ line segment cap o cap p is congruent to line segment cap r cap t Skip to navigation page 1 of 1

Question

GPT-4o mini · Answer

To establish that triangles △OPQ and △RST are congruent using the SSS (Side-Side-Side) Congruence Theorem, you need to demonstrate that all three sides of one triangle are congruent to the corresponding three sides of the other triangle.

Assuming you already have two pairings of sides that are congruent based on the given information, you need the length of the third pair of sides to be congruent. Therefore, you need:

One additional pair of sides to be congruent between the two triangles.

Based on your options, here’s a breakdown:

QO ≅ TR: If you have established OP ≅ RS and OQ ≅ ST, then having QO ≅ TR would allow you to satisfy the SSS theorem.
OQ ≅ RS: This would similarly complete the set of congruent sides needed to apply SSS.
OP ≅ RT: This completes the side criterion for SSS if you had the other two pairings as well.

Without knowing which pairs you already have congruence established for, it's difficult to determine the exact piece needed. However, you need the congruence of either QO ≅ TR, OQ ≅ RS, or OP ≅ RT as the additional piece of information.

In summary, any of those options could be correct depending on what you already have confirmed as congruent between the two triangles. If you are looking for an exact answer among the given choices, you would need to look for the one that ensures all three sides match to satisfy the SSS condition.