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.
- Determine the size of the given angle.
- Divide the measured size by two.
- 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:
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.
Now the points of intersection of the circle with the two legs of the angle are marked:
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.
There is no need to draw whole circles, as we are only interested in the intersection of the two circles. These are marked again.
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.
The method is briefly summarized here:
- With the circle becomes a circlearoundtheVertex drawn of the angle.
- The Intersections of the drawn circle with the two legs of the angle are marked.
- To both of them Marker points a circle with an identical radius is drawn in each case. The radius must be set so large that the two circles intersect.
- The two intersection points of the newly drawn circles must be marked again.
- Last will be the Intersections of the two circles we marked earlier. The line must go through the vertex of the angle. The bisector is now drawn in.
With the exercises you can practice drawing bisectors with the set square as well as with compasses and ruler. Good luck with it!
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