# Worksheet: Perpendicular Bisector Theorem and Its Converse

In this worksheet, we will practice using the perpendicular bisector and its theorem, the converse of the perpendicular bisector theorem, and the circumcenter theorem.

**Q2: **

Determine whether is a perpendicular bisector of .

- AIt is not a perpendicular bisector.
- BIt is a perpendicular bisector.

**Q3: **

In the diagram, and .

Find .

Find .

**Q4: **

In the diagram, is the perpendicular bisector of . Find the value of .

**Q5: **

What makes an intersecting line a perpendicular bisector?

- Awhen the two lines meet at a right angle and the segment of each line is consequently of equal length
- Bwhen the intersecting line divides the other into two line segments of equal length
- Cwhen the line intersects a line segment at an acute angle and divides it into two line segments of equal length
- Dwhen the line intersects a line segment at right angles and divides it into two line segments of equal length
- Ewhen the line intersects a line segment at an obtuse angle and divides it into two line segments of equal length

**Q6: **

When is a line said to be an angle bisector?

- Awhen it cuts another line segment into two equal parts
- Bwhen it divides an angle into two distinct angles
- Cwhen it cuts another line segment into two distinct parts
- Dwhen it divides an angle into two angles of equal size
- Ewhen it connects two angles