Question

1. given: b is the midpoint of \\( \overline{ac} \\).

prove: \\( ac = 2ab \\)
place the steps in order to complete the proof.
\\( \text{a} 1. \text{b} 2. \text{c} 3. \text{d} 4. \text{e} 5. \\) \\( 2ab = ac \\) (substitution)
\\( \text{a} 1. \text{b} 2. \text{c} 3. \text{d} 4. \text{e} 5. \\) b is the midpoint of segment ac. (given)
\\( \text{a} 1. \text{b} 2. \text{c} 3. \text{d} 4. \text{e} 5. \\) \\( ab + ab = ac \\) (substitution)
\\( \text{a} 1. \text{b} 2. \text{c} 3. \text{d} 4. \text{e} 5. \\) \\( ab + bc = ac \\) (segment addition postulate)
\\( \text{a} 1. \text{b} 2. \text{c} 3. \text{d} 4. \text{e} 5. \\) \\( ab = bc \\) (definition of midpoint)

Explanation:

Step1: Given information

B is the midpoint of segment AC. (Given)

Step2: Use mid - point definition

\(AB = BC\) (Definition of midpoint)

Step3: Use segment addition postulate

\(AB+BC = AC\) (Segment Addition Postulate)

Step4: Substitute \(BC\) with \(AB\)

\(AB + AB=AC\) (Substitution)

Step5: Simplify the left - hand side

\(2AB = AC\) (Substitution)

Answer:

1. B is the midpoint of segment AC. (Given)
2. \(AB = BC\) (Definition of midpoint)
3. \(AB + BC=AC\) (Segment Addition Postulate)
4. \(AB + AB = AC\) (Substitution)
5. \(2AB = AC\) (Substitution)