03.	+Segment+Bisectors

03. Segment Bisectors
By: Max Llewellyn, Lindsay Marella, and Andrea Korn

What is a Segment Bisector?
A segment bisector is something that divides a line segment in to two equal parts. 'To bisect' something generally to cut it into two equal parts; the 'bisector' is the thing doing the cutting. IE: In this example, the vertical line is the segment bisector. It is bisecting the horizontal line between the two circles, dividing it in to two equal halves. As is shown in this diagram, **segment bisectors** can come in the form of **line segments, planes,** or **points,** as well as **rays** or **lines**. Look at the example in the lower left-hand corner. Segment JP intersects segment HK to create two congruent segments, segment HP and segment PK. This isn't much different from when a plane is a segment bisector. The plane, as is shown in the bottom example of the right-hand side, bisects the line segment to create two congruent segments.

If a segment is crossed at a right angle to form two congruent segments, it is called a **perpendicular bisector**. This is shown in the diagram in the bottom left-hand corner. Java plug-in Version 1.4 or later required.
 * Midpoints** are also very important when discussing segment bisectors. A **midpoint** is the point where the bisector crosses to form two perpendicular segments. For example, in the diagram featured in the top left-hand corner, point B is the midpoint.


 * It is important to note that **lines** or **planes** cannot be bisected, as they have no definite boundaries.

Example Problems:

 * 1.** Find the value of NM if point M bisects segment NO, and segment NO has a length of 4.

The value of NM is 2.

Answer: 4 units have the length of 10 units.
 * 2.**
 * 3.** Segment AB and CD are both 20 units long and bisect each other. How many segments have a length of 10 units?

Worksheet
Without answers: With answers:

Helpful Links
http://www.mathopenref.com/bisectorline.html http://teachers.henrico.k12.va.us/math/ms/C1Files/04Geometry/4-3Bisectors.html http://www.mathopenref.com/bisectorline.html