Segment Bisector Lesson - Definition, Types, Midpoint & Perpendicular Bisector

Lesson Overview

• What Is a Segment Bisector?
• Types of Segment Bisectors
• How to Construct a Segment Bisector: Using a Compass and Ruler
• Segment Bisector and Midpoints
• Segment Bisectors and Perpendicular Bisectors
• Segment Bisector Assessment

Segment bisectors explore how lines are divided into two equal parts by a point on the line. They are fundamental in geometry and have applications in constructing shapes, solving equations and understanding geometric properties.

What Is a Segment Bisector?

A segment bisector is a line, segment, ray, or plane that bisects a line into two equal parts at its midpoint. When a segment bisector intersects a line segment, it does so at a 90-degree angle if it is a perpendicular bisector, ensuring symmetry and balance. 

Diagram illustrates the concept of a segment bisector

Line segment AB has two endpoints, A and B. Point X is the midpoint of AB, dividing it into two equal parts, AX and XB. A vertical line intersects point X at a 90-degree angle.

Types of Segment Bisectors

• Points: A segment's midpoint is determined by its points, which split it in half. 

• Lines: A line can be drawn through a segment to create two parallel parts that share the same length. 

• Line Segment: Any line that passes through the midpoint of the segment. It doesn't have to be perpendicular.

• Perpendicular Bisector: A line that intersects the segment at its midpoint and forms a right angle.

• Ray Bisector: Parts of a line with one endpoint and extending infinitely in one direction.

Take this quiz -

Math Quiz: Bisect Line Segments and Angles.

How to Construct a Segment Bisector: Using a Compass and Ruler

Step 1: Draw the Line Segment

Begin by drawing the line segment you want to bisector. Label its endpoints as A and B.

Step 2: Set the Compass Width

Open your compass wider than half the length of the segment.

Step 3: Draw Arcs from Both ends

Place the compass at point A and draw an arc above and below the line segment. Repeat this step from point B without changing the compass width. The arcs should intersect.

Step 4: Mark the Intersection Points

Label the points where the arcs intersect as C and D.

Step 5: Draw the Bisector

Use a ruler to draw a straight line passing through points C and D. This line is the bisector of the segment AB.

Take this quiz :

Geometry: Segment Questions! Trivia Quiz

Segment Bisector and Midpoints

The midpoint is a key feature of any segment bisector. A midpoint divides a segment into two equal parts and serves as the intersection point for a bisector.

Formula for the Midpoint:

For a segment with endpoints at coordinates (Ax, Ay) and (Bx, By), the midpoint M is calculated as: M = ((Ax + Bx) / 2, (Ay + By) / 2)

Segment Bisectors and Perpendicular Bisectors

A perpendicular bisector is a specific type of segment bisector that is particularly important in geometry. It not only divides a segment into two equal halves but also forms a right angle with the segment.

Key Features:

• Equidistant Points: Any point on the perpendicular bisector is equidistant from the endpoints of the segment.
• Application in Triangles: Perpendicular bisectors are used to find the circumcenter of a triangle.
  

Segment Bisector Assessment

1. If a segment is 8 cm long and a line bisects it, how long is each half?
2. A gardener wants to divide a 12-foot-long flower bed into two equal sections. How can they use a segment bisector to do this?
3. Match the term with its definition:

Answers:

1. If a segment is 8 cm long and a line divides it, each half will be 4 cm long.
2. The gardener can find the midpoint of the flower bed by measuring 6 feet from either end. This midpoint marks the segment bisector, dividing the flower bed into two equal sections.
3. Match the term with its definition: