Geometry How to bisect an angle

Construct and draw the bisector

method

1. With the set square

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

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  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:

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  1. With the circle becomes a circlearoundtheVertex drawn of the angle.

  2. The Intersections of the drawn circle with the two legs of the angle are marked.

  3. 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.

  4. The two intersection points of the newly drawn circles must be marked again.

  5. 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!