# Geometry How to bisect an angle

## Construct and draw the bisector

### 1. With the set square

If we are allowed to use a set square, drawing a bisector is very easy.

1. Determine the size of the given angle.

2. Divide the measured size by two.

3. Measure and draw the calculated angle size on one of the two sides of the angle.

### 2. With a compass and a ruler

This angle should be divided into two halves of exactly the same size. A compass and a ruler are available as aids. Let's take a look at the procedure in detail here:

Illustration of the angle to be split

First, a circle is drawn around the vertex of the angle. To do this, start with the compass at the vertex and draw a circle around it.

Figure: Circle around the intersection of the angle

Now the points of intersection of the circle with the two legs of the angle are marked:

Illustration: Intersections \$ E \$ and \$ F \$ of the circle with the legs of the angle

A circle is drawn again around the two intersection points. The radius of the two circles must be the same. To do this, start with the compass point in the intersection points (here points \$ E \$ and \$ F \$). The radius must be set so large that the two circles overlap.

Illustration of two circles around the intersection points

There is no need to draw whole circles, as we are only interested in the intersection of the two circles. These are marked again.

Figure: Mark the intersection of the two circles

Now we come to the last step. The two points of intersection (here \$ G \$ and \$ H \$) must now be connected by a straight line. This straight line divides the angle into two halves of equal size and runs through the vertex of the angle \$ \ rightarrow \$ bisector.

Figure: Draw the bisector

The method is briefly summarized here: