In triangle RST above, RS = RT. Which of the following must be true?

Rationale

s = t

In triangle RST, where RS = RT, the property of isosceles triangles dictates that the angles opposite the equal sides must also be equal. Therefore, the angles at points S and T, denoted as s and t, must be equal, confirming that s = t.

A (ST = RS) YOUR ANSWER

This statement does not need to be true. In an isosceles triangle, the lengths of the base (ST) can differ from the lengths of the equal sides (RS and RT). Therefore, while ST can be equal to RS in some cases, it is not a requirement.

B (RT > ST) YOUR ANSWER

This choice is incorrect because the relationship between the sides does not dictate that RT must be greater than ST. Depending on the specific dimensions of triangle RST, RT could be equal to, less than, or greater than ST.

C (s = t) CORRECT

This statement is true as it reflects the property of isosceles triangles, where the angles opposite the equal sides are equal. Since RS = RT, the angles at S and T, labeled s and t, must indeed be equal.

D (r > t) YOUR ANSWER

This is not necessarily true, as the angle at R (r) can be less than, equal to, or greater than the angles at S and T (s and t). The relationship between these angles is not strictly defined without specific measures.

E (s > r) YOUR ANSWER

This statement is also not guaranteed. The angles in triangle RST do not have a defined order solely based on the side lengths, and s could be less than, equal to, or greater than r.

Conclusion

In triangle RST, the equality of sides RS and RT directly leads to the conclusion that the angles opposite these sides, s and t, must be equal. Therefore, s = t is the only statement that must hold true, while the other options present relationships that are not guaranteed by the properties of isosceles triangles.

In triangle RST above, RS = RT. Which of the following must be true?

s = t

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