Constructing a Perpendicular Bisector

Hi everyone and welcome to MathSux! In this post we are going to be constructing a perpendicular bisector, a line that cuts a line segment in half and creates four 90º angles. It’s a super fast and super simple construction! If you’re looking for more 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 ?

  • Cut’s our line AB in half at its midpoint, creating two equal halves.
  • This will also create four 90º angles about the line.
Constructing a Perpendicular Bisector

What is happening in this GIF?

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

Step 2: Next we are going to place the compass on point A and swing above and below line AB to make 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 and repeat the same step we did on point A, drawing a semi circle.

Step 4: Notice the intersections above and below line AB!? Now, we want to connect these two points by drawing a line with a ruler or straight edge.

Step 5: Yay! We now have a perpendicular bisector! This cuts line AB right at its midpoint, dividing line AB into two equal halves.  It also creates four 90º angles.

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 in this post. 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!

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