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

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

OQ¯¯¯¯¯¯¯¯≅RS¯¯¯¯¯¯¯
Modifying above upper O upper Q with bar congruent to Modifying above upper R upper S 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 use the SSS (Side-Side-Side) Congruence Theorem to state that triangles \( \triangle OPQ \cong \triangle RST \), we need all three corresponding sides to be congruent.

Since two sides are already marked as congruent, we need one more piece of information that states the congruence of one of the remaining pairs of sides.

The options you provided indicate possible congruences for the remaining sides:

1. \( \overline{OP} \cong \overline{RT} \)
2. \( \overline{OQ} \cong \overline{RS} \)
3. \( \overline{PQ} \cong \overline{RT} \)
4. \( \overline{QO} \cong \overline{TR} \)

Since we have already two pairs of congruent sides, we need the congruence of the third side. The appropriate addition to state \( \triangle OPQ \cong \triangle RST \) by SSS would typically require:

• If \( OP \) and \( RT \) are congruent, we could choose \( \overline{OQ} \cong \overline{RS} \) or \( \overline{PQ} \cong \overline{ST} \).

If \( OQ \cong RS \) is required, we need to select that pair:

The answer is: \( \overline{OQ} \cong \overline{RS} \).