Questions: Given: The line OL bisects the line segment AB at point O and A-O-B Prove: The measure of line segment AO equals the measure of line segment OB

Given: The line OL bisects the line segment AB at point O and A-O-B Prove: The measure of line segment AO equals the measure of line segment OB
Transcript text: Given: $\overleftrightarrow{O L}$ bisects $\overline{A B}$ at point $O$ and $A-O-B$ Prove: $m \overline{A O}=m \overline{O B}$
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Solution

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The answer is: The definition of a segment bisector.

Explanation:

  1. Definition of a Segment Bisector: A segment bisector is a line, segment, ray, or plane that divides a segment into two equal parts. In this problem, the line \(\overleftrightarrow{O L}\) is given to bisect the segment \(\overline{A B}\) at point \(O\). This means that point \(O\) divides \(\overline{A B}\) into two equal segments, \(\overline{A O}\) and \(\overline{O B}\).

  2. Application to the Problem: Since \(\overleftrightarrow{O L}\) bisects \(\overline{A B}\) at point \(O\), by the definition of a segment bisector, the segments \(\overline{A O}\) and \(\overline{O B}\) must be equal in length. Therefore, \(m \overline{A O} = m \overline{O B}\).

In summary, the definition of a segment bisector justifies the statement that the measures of segments \(\overline{A O}\) and \(\overline{O B}\) are equal.

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