Use the image to answer the question.

Question

An illustration shows two congruent triangles in different orientations. Two corresponding sides are marked as congruent.

What additional piece of information is needed in order to state that △OPQ≅△RST by the SSS Congruence Theorem?

(1 point)
Responses

OQ¯¯¯¯¯¯¯¯≅RS¯¯¯¯¯¯¯
Modifying above upper O upper Q with bar congruent to Modifying above upper R upper S with bar

OP¯¯¯¯¯¯¯¯≅RT¯¯¯¯¯¯¯
Modifying above upper O upper P with bar congruent to Modifying above upper R upper T with bar

PQ¯¯¯¯¯¯¯¯≅RT¯¯¯¯¯¯¯
Modifying above upper P upper Q with bar congruent to Modifying above upper R upper T with bar

QO¯¯¯¯¯¯¯¯≅TR¯¯¯¯¯¯¯

Answer 1

To state that triangles \( \triangle OPQ \cong \triangle RST \) by the SSS (Side-Side-Side) Congruence Theorem, we need to ensure that all three corresponding sides of the two triangles are congruent. Since two sides are already marked as congruent, we need the third side to also be congruent to complete the criteria for SSS.

Thus, we need one additional piece of information that states the length of the third sides of the two triangles are congruent.

From the provided options:

• OQ ≅ RS would give us the third congruence.
• OP ≅ RT is not useful as we already have two other sides confirmed.
• PQ ≅ RT does not form a complete set for SSS with given sides.
• QO ≅ TR does not relate correctly for the congruence needed.

Therefore, the correct response is:

OQ ≅ RS.

This confirms the congruence of all three sides needed for SSS theorem.