Match the reasons to complete the proof. Given: AB=28, m lies on the line AB Prove: m is the midpoint

Answer 1

To complete the proof that \( m \) is the midpoint of \( AB \), you would typically follow a logical sequence. Here’s how you might match reasons with statements in the proof:

1. Given: \( AB = 28 \)
   Reason: This is a statement of the given information.

2. Definition of Midpoint: A point \( m \) is the midpoint of segment \( AB \) if \( AM = MB \) and \( AB = AM + MB \).
   Reason: Definition of a midpoint.

3. Assume \( AM + MB = AB \): Since \( m \) lies on line \( AB \), we can express \( AM + MB \) where \( AM \) and \( MB \) are the lengths from \( A \) to \( m \) and \( m \) to \( B \).
   Reason: Segment addition postulate.

4. Set up the equation using the given length: If \( m \) is the midpoint, \( AM = MB \). Hence, \( AM + MB = 2(AM) = 28 \).
   Reason: Substitution based on the assumption.

5. Solve for \( AM \): \( 2(AM) = 28 \) implies \( AM = 14 \) and \( MB = 14 \).
   Reason: Algebraic manipulation.

6. Conclude: Since \( AM = MB \) and both are equal to \( 14 \), by definition, \( m \) is the midpoint of \( AB \).
   Reason: The conclusion follows from the definition of a midpoint.

By following these steps, you can successfully complete the proof that \( m \) is indeed the midpoint of \( AB \).