Question

proof
statements reasons

1. sr = rt 1. ?
2. ? 2. definition of mid - point
3. sr = ur and rt = rv 3. ?
4. ? 4. substitution
5. r is the mid - point of uv. 5. ?

keyboard help

Explanation:

Step1: Identify given statement reason

Since $SR = RT$ is the first - given statement, the reason for it is "Given".

Step2: Determine statement for mid - point definition

If $R$ is the mid - point of some segment (let's assume $ST$), then the statement for the "Definition of mid - point" could be "$R$ is the mid - point of $\overline{ST}$".

Step3: Identify reason for $SR=UR$ and $RT = RV$

The reason for $SR = UR$ and $RT=RV$ is likely "Given" (if these equalities are given facts in the overall problem context).

Step4: Determine substitution statement

Since $SR = RT$, $SR = UR$ and $RT = RV$, by substitution, we can get $UR=RV$.

Step5: Identify reason for $R$ being mid - point of $\overline{UV}$

The reason for "$R$ is the mid - point of $\overline{UV}$" is "Definition of mid - point" because we have shown $UR = RV$.

Answer:

1. Given
2. $R$ is the mid - point of $\overline{ST}$
3. Given
4. $UR = RV$
5. Definition of mid - point