2. If AB is the perpendicular bisector of IK, which statement can be concluded from the given information?
a. AB = IK
b. AJ = IJ
c. BI = BK
d. BI = AK
To find the correct statement that can be concluded from the given information, let's first understand what it means for AB to be the perpendicular bisector of IK.
A perpendicular bisector is a line that passes through the midpoint of a line segment and is perpendicular to it. In this case, AB is the perpendicular bisector of IK, which means that AB cuts IK into two equal halves, and AB is perpendicular to IK.
From this information, we can conclude that the statement "c. BI = BK" is correct. Since AB is the perpendicular bisector of IK, it intersects IK at its midpoint. Therefore, the line segment IB is equal in length to the line segment BK because they are both halves of the same line segment (IK).
To arrive at this conclusion, you can visualize the situation by drawing a diagram:
1. Draw a line segment IK.
2. Draw a line AB that intersects IK at its midpoint (the point where AB cuts IK exactly in half).
3. Make sure that AB is perpendicular to IK (forming a right angle).
4. Label the intersection point of AB and IK as point J.
5. Label the points where AB intersects IK as points I (on the left) and K (on the right).
6. Observe that IB is equal in length to BK because they are both halves of the line segment IK.
By understanding the concept of perpendicular bisectors and visually analyzing the situation, we can conclude that BI = BK based on the given information.