Statement 1: 2AB = AC
Reason 1: Given
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Statement 2: AC = AB+BC
Reason 2: Segment addition postulate (which your teacher abbreviated to "Seg + Post")
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Statement 3: 2AB = AB+BC
Reason 3: Substitution
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Statement 4: 2AB-AB = AB+BC-AB
Reason 4: Subtraction Property of Equality
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Statement 5: AB = BC
Reason 5: Combine like terms
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Notes:
- The first reason is "given" since we just simply restate what the instructions provide. If you are given multiple items, you list each one at a time.
- The segment addition postulate is where we break a line into smaller parts and then build it back together.
- Substitution is simply replacement. We've replaced AC with 2AB.
- The subtraction property of equality is the idea where we subtract the same thing from both sides. In statement 4, we're subtracting AB from both sides.
- The last statement of any proof is always the thing we're trying to prove. Once we reach such a statement, there's no need to go any further since the proof has concluded.
