Question
Line segment XY¯¯¯¯¯¯¯¯ is a perpendicular bisector of segment AB¯¯¯¯¯¯¯¯ , with the two segments meeting at point O . What is true about OB¯¯¯¯¯¯¯¯ ?
Answers
GPT-4o mini
Since line segment \( XY \) is the perpendicular bisector of segment \( AB \) at point \( O \), it has several important properties:
1. **Perpendicularity**: \( XY \) is perpendicular to \( AB \) at point \( O \). This means that the angles formed at point \( O \) between line \( XY \) and segment \( AB \) are right angles (90 degrees).
2. **Bisection**: Since \( O \) is the midpoint of segment \( AB \), it divides \( AB \) into two equal segments. Thus, the segments \( AO \) and \( OB \) are equal in length. This means \( AO = OB \).
Therefore, the statements true about \( OB \) are:
- \( OB \) is equal to \( AO \) (i.e., \( OB = AO \)).
- \( O \) is the midpoint of segment \( AB \).
In summary, the key fact about \( OB \) is that \( OB = AO \) and that \( O\) is the midpoint of segment \( AB \).
1. **Perpendicularity**: \( XY \) is perpendicular to \( AB \) at point \( O \). This means that the angles formed at point \( O \) between line \( XY \) and segment \( AB \) are right angles (90 degrees).
2. **Bisection**: Since \( O \) is the midpoint of segment \( AB \), it divides \( AB \) into two equal segments. Thus, the segments \( AO \) and \( OB \) are equal in length. This means \( AO = OB \).
Therefore, the statements true about \( OB \) are:
- \( OB \) is equal to \( AO \) (i.e., \( OB = AO \)).
- \( O \) is the midpoint of segment \( AB \).
In summary, the key fact about \( OB \) is that \( OB = AO \) and that \( O\) is the midpoint of segment \( AB \).