Final answer:
To prove that ST > RT, we can use the given information and the properties of triangles and angles. By establishing the congruence of certain angles and using the angle-side-angle (ASA) congruence theorem, we can conclude that triangle STX is congruent to triangle TRS. From this congruence, it follows that ST > RT.
Step-by-step explanation:
To prove that ST > RT, we can use the given information and the properties of triangles and angles. Let's begin:
1. Given: RX = XS; m/SXT = 97
2. We know that RX = XS, so we can say that angle X is congruent to angle S. Therefore, m/XTS = 180 - m/SXT = 180 - 97 = 83.
3. In triangle XTS, we have angle X congruent to angle S, so we can conclude that TX = XS = RX. Therefore, angle TRS is congruent to angle STX.
4. By the angle-side-angle (ASA) congruence theorem, we can say that triangle TRS is congruent to triangle STX.
5. Since the corresponding sides of congruent triangles are congruent, we have RT = TS.
6. In triangle STX, we have RT = TS and angle TRS congruent to angle STX. Therefore, ST > RT.
7. Hence, we have proven that ST > RT using the given information and triangle congruence properties.