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

QO¯¯¯¯¯¯¯¯≅TR¯¯¯¯¯¯¯
Modifying above upper Q upper O with bar congruent to Modifying above upper T upper R with bar

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¯¯¯¯¯¯¯

Answer 1

To state that \( \triangle OPQ \cong \triangle RST \) by the SSS (Side-Side-Side) Congruence Theorem, you need to establish that all three sides of one triangle are congruent to the corresponding three sides of the other triangle.

Since two corresponding sides are already marked as congruent, you need to find the additional side that corresponds with these two that is also congruent.

The correct additional piece of information that is needed would be:

OP¯¯¯¯¯¯¯¯≅RT¯¯¯¯¯¯¯

This implies that the third corresponding sides are also congruent, allowing the application of the SSS Congruence Theorem to conclude that the triangles are congruent.