Bisect a Line Segment

Hi everyone and welcome to MathSux! In this post we are going to be constructing a perpendicular bisector by using a compass and stright edge. A perpendicular bisector, (also known as a segment bisector), is a line that cuts a line segment in half and creates four 90º angles. It is a super fast and super simple construction! We’ll also go over the Perpendicular Bisector Theorem we can infer from our original construction. If you’re looking for more geometric constructions, don’t forget to check more out here. Thanks so much for stopping by and happy calculating! 🙂

What is the Perpendicular Bisector of a line segment?

  • A perpendicular bisector slices our line segment AB (or any line segment) in half at its midpoint, creating two equal halves.
  • This will also create a 90º angle ( or right angle) about the line.
Constructing a Perpendicular Bisector through line segment AB

What is happening in this GIF?

Step 1: Notice we are given line segment AB. First, we are going to measure out a little more than halfway across the line segment AB by using a compass.

Step 2: Next we are going to place the point of the compass on point A and swing above and below line segment AB to create a half circle.

Step 3: Keeping the same distance on our compass, we are then going to place the point of the compass onto Point B (the opposite side) and repeat the same step we did on point A, drawing an arc in the shape of a semi-circle.

Step 4: Notice the intersection point above and below line segment AB!? Now, we are going to connect these two points by drawing a line with a ruler or straightedge.

Step 5: Yay! We now have a segment bisector! This cuts line segment AB right at its midpoint, while also dividing line segment AB into two equal halves and creating a 90º angle around our two intersecting lines.

Perpendicular Bisector Theorem:

The Perpendicular Bisector Theorem explains that any point along the perpendicular bisector line we just create is equidistant to each end point of the original line segment (in this case line segment AB).

Therefore, if we were to draw points C,D, and E along the perpendicular bisector, then draw imaginary lines stemming from these points to each end point, we’d get something like the image below:




Line Segment Theorem

Notice that with each of our points on the perpendicular line above, we can now state that the following is true:




The fact that we can state the above is true is reason for the Perpendicular Bisector Theorem!

Constructions and Related Posts:

Looking to construct more than just a perpendicular segment bisector? Check out these related posts and step by step tutorials on geometry constructions below!

Construct an Equilateral Triangle

Perpendicular Line through a Point

Angle Bisector

Construct a 45º angle

Altitudes of a Triangle (Acute, Obtuse, Right)

Construct a Square inscribed in a Circle

Best Geometry Tools!

Looking to get the best construction tools? Any compass and straight edge will do the trick, but personally, I prefer to use my favorite mini math toolbox from Staedler. Stadler has a geometry math set that comes with a mini ruler, compass, protractor, and eraser in a nice travel-sized pack that is perfect for students on the go and for keeping everything organized….did I mention it’s only $7.99 on Amazon?! This is the same set I use for every construction video! Check out the link below and let me know what you think!

Still got questions? No problem! Don’t hesitate to comment with any questions below or check out the video above. Thanks for stopping by and happy calculating! 🙂

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Want to see how to construct a square inscribed in a circle? Or maybe you want to construct an equilateral triangle? Click on each link to view each construction! And if you’re looking for even more geometry constructions, check out the link here! And if you’re looking for a construction you don’t yet see, please be sure to suggest it in the comments below!

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