Line Upper A Upper B intersects line segment Upper I Upper K at point Upper J. Text reads: Given Modifying Above Upper A Upper B with two-way-arrow is the perpendicular bisector of Modifying Above Upper I Upper K with bar.
Question
Which statement can you conclude is true from the given information?
(1 point)
Responses
AI = KB
AI = KB
AI = AK
AI = AK
AB = IK
AB = IK
AJ = JB
AJ = JB
From the given information, we can conclude that AJ = JB.
To determine which statement can be concluded as true, we need to analyze the given information about the intersection of line AB and line segment IK at point J.
The given information states that line AB, with two-way-arrow, is the perpendicular bisector of line segment IK, represented by a line with a bar over it.
To understand the concept of a perpendicular bisector, we can break it down as follows:
- A perpendicular bisector is a line that intersects a line segment at a 90-degree angle (perpendicular) and divides it into two equal halves (bisector).
Based on this understanding, we can draw some conclusions:
1. AI = AK: Since line AB is the perpendicular bisector of line segment IK, it implies that point J is on the line AB and divides line segment IK into two equal halves. Therefore, the lengths of AI and AK are equal.
2. AB = IK: Since line AB is the perpendicular bisector of line segment IK, it implies that point J is on the line AB and divides line segment IK into two equal halves. Therefore, the lengths of line segment IK and line segment AB are equal.
However, we cannot conclude that AJ = JB from the given information about the perpendicular bisector. The perpendicular bisector ensures that line segment IK is divided into two equal halves, but it does not provide any information about the relative positions of point J, point A, and point B along the line segment.
Therefore, the statement that can be concluded as true from the given information is:
AB = IK