Question

In triangles ghi and rst, if g= r, h = s, and gi = rt, is this information sufficient to prove triangles ghi and rst congruent through sss? Explain your answer.

1) Yes, because all three sides of the triangles are equal.
2) No, because we also need to know the measures of the angles.
3) Cannot be determined with the given information.
4) Not enough information provided.

Answer 1

The information provided is not sufficient to prove SSS congruence between triangles ghi and rst.

Step-by-step explanation:

The information provided is not sufficient to prove that triangles ghi and rst are congruent through SSS (Side-Side-Side) congruence.

In order to prove SSS congruence, all three pairs of corresponding sides must be equal in length. While we know that g=r, h=s, and gi=rt, we do not have information about the remaining sides of the triangles. Without this additional information, we cannot determine if the triangles are congruent.

Therefore, the correct answer is option 4: Not enough information provided.