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In triangle RST, the sides opposite equal angles are equal.

In triangle RST, since RS = RT, it follows that the angles opposite these sides must also be equal. Therefore, the measures of the angles at points S and T must be equal, leading to the conclusion that s = t.

A) ST = RS

This option is incorrect because while RS and RT are equal, there is no direct relationship established between ST and RS solely based on the information given about triangle RST. The lengths of ST could vary independently.

B) RT > ST

This option is also incorrect. The equality of sides RS and RT does not imply that RT is greater than ST. Without specific measurements or additional information, it cannot be concluded that one side is longer than another.

C) s = t

This option is correct because, in triangle RST, the equality of the sides RS and RT indicates that the angles opposite these sides, namely angles S and T, must be equal. Therefore, s, the measure of angle S, must indeed equal t, the measure of angle T.

D) r > t

This option is incorrect as it suggests a relationship between angle R and angle T without sufficient information. The fact that RS equals RT does not provide any basis for comparing angle R with angle T.

E) s > r

This option is incorrect as well. There is no evidence from the information provided to conclude that angle S is greater than angle R. The equality of sides RS and RT does not imply any specific relationship between angle S and angle R.

Conclusion

The correct answer is C, as it accurately reflects the properties of isosceles triangles where equal sides correspond to equal angles. All other options fail because they either misinterpret the relationships within the triangle or lack sufficient justification based on the given information.