prove: ST =TS

Question

prove: △ RST = △ UTS

Answer 1

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.