Answer:
Explanation:
1. Given: ST = UT (Given statement)
2. ZRST = 2 (Given statement)
To complete the 2-column proof, we need to provide statements and reasons for each step.
3. ST = UT (Given statement)
Reason: Reflexive Property of Equality - Any quantity is equal to itself.
4. ZRST = ZRUT (Substitution Property of Equality)
Reason: When two things are equal, you can replace one with the other.
5. ZRUT = 2 (Transitive Property of Equality)
Reason: If two quantities are equal to the same quantity, then they are equal to each other.
6. LRTS ZVTU (Vertical Angles Theorem)
Reason: Vertical angles are congruent, meaning they have equal measures.
7. ARST = AVUT (Substitution Property of Equality)
Reason: When two things are equal, you can replace one with the other.
So, the completed 2-column proof is:
Statement Reason
1. ST = UT Given
2. ZRST = 2 Given
3. ST = UT Reflexive Property of Equality
4. ZRST = ZRUT Substitution Property of Equality
5. ZRUT = 2 Transitive Property of Equality
6. LRTS ZVTU Vertical Angles Theorem
7. ARST = AVUT Substitution Property of Equality