Final answer:
From the fact that IJ is the perpendicular bisector of AB, we can conclude AJ = BJ. No conclusion can be made regarding IJ being a right angle, IJ being equal to JK, or A being the midpoint of B. Option A is correct.
Step-by-step explanation:
The question involves understanding properties of geometric figures, specifically lines and angles. Given that IJ is the perpendicular bisector of AB, we can conclude that AJ = BJ which makes statement a true. When a line segment is bisected perpendicularly, it means that each half is equal in length and that the bisector creates a right angle with the line segment it bisects.
However, the other statements b, c, and d cannot be concluded based on the given information alone. Notably, the statement that IJ is a right angle refers to the relationship between two lines, not the segment itself, and A being the midpoint of B is not possible, as a point cannot be the midpoint of another point.
The statement that can be concluded as true from the given information is a) AJ=BJ.
According to the given information, IJ is the perpendicular bisector of AB. This means that IJ divides AB into two equal halves, and since J is the midpoint of AB, AJ and BJ are equal.
Therefore, the correct statement is a) AJ=BJ.