prove: ST =TS
prove: △ RST = △ UTS
1. Given: Triangle RST and Triangle UTS, where ST = TS
To prove: Triangle RST is congruent to Triangle UTS
Proof:
Since ST = TS, triangle RST is an isosceles triangle with base RT.
By the Isosceles Triangle Theorem, the angles opposite the congruent sides of an isosceles triangle are congruent.
Therefore, angle RST = angle TST (Since ST = TS)
Similarly, angle UTS = angle STU (Since ST = TS)
Since angle RST = angle TST and angle UTS = angle STU, by Angle-Angle-Side (AAS) congruence theorem, triangle RST is congruent to triangle UTS.
Thus, △ RST = △ UTS.