Angle Bisector Definition & Example

Hi everyone and welcome to another fabulous week of MathSux! I bring to you the first construction of the back-to-school season! In this post, we are going to go over the angle bisector definition and example. First, we will define what an angle bisector is, then we’ll take our handy dandy compass and straight edge to construct an angle bisector that will bisect an angle for any size! Check out the video and GIF below for more and happy calculating! 🙂

What is an Angle Bisector?

An Angle Bisector is a line that evenly cuts an angle into two equal halves, creating two equal angles. For example, if we have a 70-degree acute angle and we create an angle bisector this would create two equal angles of 35 degrees each, dividing 70 by 2. Check out how to do this construction step by step with pictures and explanations below.

Angle Bisector Example:

Angle Bisector Definition & Example

Step 1: First, we start by placing the point of our compass on the point of the angle, which in this case is 70 degrees.

Step 2: Next, we are going to draw an arc that intersects both lines that stem from the angle we want to bisect.

Step 3: Now, take the point of our compass to where the lines and arc intersect, and draw an arc towards the center of the angle.

Step 4: Keeping that same distance on our compass, we are going to take the point of your compass and place it on the other point where both the line and arc intersect, and draw another arc towards the center of the angle.

Step 5: Notice we made an intersection!? Where these two arcs intersect, mark a point and using a straight edge or ruler, connect it to the center of the original angle. 

Step 6: We have officially bisected our angle into two equal 35-degree halves, creating an angle bisector!

*Please note that the above example bisects a 70º angle, but this construction method will work for an angle of any size acute or obtuse!🙂

What do you think of the above angle bisector definition & example? Do you use a different method for construction? Let me know in the comments below! 🙂

Constructions and Related Posts:

Looking to construct more than just an angle bisector? Check out these related posts and step-by-step tutorials on geometry constructions below!

Construct an Equilateral Triangle

Perpendicular Line through a Point

Bisect a Line Segment with Perpendicular 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 in this post. Check out the link below and let me know what you think!

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Looking for more constructions? Check out how to construct a square inscribed in a circle and an equilateral triangle by clicking on their respective links! And if you’re looking for even more geometry constructions, check out the link here!

AnAngle Bisector Definition & Example

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