Answer:
Here are the completed proofs with the missing statements and reasons:
Proof 1:
Given: RS = 1/2RT
Prove: S is the midpoint of RT
Statements:
1. RS = 1/2RT (Given)
2. 2RS = RT (Multiplication Property of Equality)
3. RS + RS = RT (Addition Property of Equality)
4. RS = RT (Definition of Midpoint)
5. S is the midpoint of RT (Definition of Midpoint)
Proof 2:
Given: M is the midpoint of LN, N is the midpoint of MO
Prove: LM = MO
Statements:
1. M is the midpoint of LN (Given)
2. MN = NO (Definition of Midpoint)
3. N is the midpoint of MO (Given)
4. LM = MN + NO (Segment Addition Postulate)
5. LM = MO (Substitution Property)
Reasons for Proof 1:
1. Given
2. Multiply both sides by 2
3. Add RS to both sides
4. Definition of midpoint
5. Definition of midpoint
Reasons for Proof 2:
1. Given
2. Definition of midpoint
3. Given
4. Segment Addition Postulate
5. Substitution Property
Explanation: