Final answer:
To justify the last two steps of the proof: RS = UT, RT = US, and we need to prove: RST = UTS. By substituting the given equalities into the expressions, we can show that RST = UTS.
Step-by-step explanation:
To justify the last two steps of the proof, we need to use the given equalities. The given information states that RS = UT and RT = US. Let's use these equalities to show that RST = UTS.
Starting with RST, we can write it as RS + ST. Using the first equality, RS can be replaced with UT, giving us UT + ST. Rearranging the terms, we have UT + TS. Now, using the second equality, we can replace TS with SR, giving us UT + SR.
Now, let's consider UTS. We can write it as UT + TS. Using the second equality, we can replace TS with SR, giving us UT + SR. As we can see, RST = UTS, which completes the proof.