1. **Problem Statement:** We are given two triangles, GHI and RST, with the following congruences: \(\angle G \cong \angle R\), \(\angle H \cong \angle S\), and segment \(GI \cong RT\). We need to determine if this information is sufficient to prove the triangles congruent by the Side-Side-Side (SSS) criterion. 2. **Recall the SSS Criterion:** The SSS criterion states that two triangles are congruent if all three pairs of corresponding sides are congruent. 3. **Given Information:** We have two pairs of congruent angles and one pair of congruent sides: - \(\angle G \cong \angle R\) - \(\angle H \cong \angle S\) - \(GI \cong RT\) 4. **Analysis:** To use SSS, we need three pairs of corresponding sides congruent. Here, only one pair of sides \(GI\) and \(RT\) is given as congruent. The other two sides are not mentioned. 5. **Conclusion:** Since only one pair of sides is congruent, and the other information is about angles, this is not sufficient to prove congruence by SSS. We would need all three pairs of sides congruent. **Final answer:** No, the given information is not sufficient to prove triangles GHI and RST congruent through SSS because only one pair of sides is congruent, and SSS requires all three pairs of sides to be congruent.