1. Bisecting Line Segments and Angles
Slideshow 40, Mathematics
Mr Richard Sasaki

2. Objectives
Learn how to bisect a line segment with a perpendicular line
Learn how to bisect an angle

3. Line segment bisection
With the use of a compass, we can bisect a line segment with a line perpendicular to this.
Let’s draw an 8cm line segment 𝑃𝑄 being bisected by a perpendicular line 𝑅𝑆 .
First, draw an 8cm line segment 𝑃𝑄 .

4. Line segment bisection
Next, with the compass we measure anywhere over half of the length of 𝑃𝑄 .
With this radius, from P, we draw a mark above and below the diagram where each mark contains the half-way point on either side.

5. Line segment bisection
Keeping the compass at the same radius, we place the point at Q and again draw marks above and below the line segment that hopefully cross.
We would then connect the crosses together to make a perpendicular line. R S
Try the worksheet!

6. 𝑅 𝑃 𝑄 𝑆 𝐶 𝐴 𝑀 𝐵 𝐶 𝐵 𝐴

7. Bisecting Angles
To bisect an angle (∠𝑃𝑄𝑅), we first mark two line segments 𝑃𝑄 , 𝑅𝑄 (or lines or rays) the same distance from the angle to be bisected.
(This can be one arc if preferred.)
From each mark made, we then make marks between the line segments, where you think the bisection will go (in the middle). S
Finally, draw the ray (or whatever) and label it!

8. 5 𝑐𝑚 𝑆

9. 𝐶