VIDEO: Constructing the bisector with a compass and ruler

Side bisector in a triangle - you should know that

• Side bisectors in the triangle are special lines that are located within the triangle. They connect the center point of one side of the triangle with the opposite corner point.
• Each triangle has accordingly three bisectors. These three bisectors intersect at a point that lies within the triangle. This point is the so-called. Center of gravity of the triangle.
• If you cut the triangle out of paper and support it at this point with a needle, it will stay flat in the air. One can imagine that the whole weight of the triangle is united in the center of gravity.

Construct side bisector

In the following, the so-called. classic construction with compasses and ruler is explained, so distances are neither measured with a ruler nor cut in half. The ruler is only used to draw a straight line or is used to (straight) connect two points.

1. Any triangle is the starting point for the construction. Avoid choosing an equilateral or isosceles triangle.


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2. Since the bisector connects the midpoint of one side of the triangle with the opposite corner of the triangle, the task at hand amounts to constructing the center of one side of the triangle with a compass and ruler.
3. So choose a side of the triangle.
4. Draw an equal (!) Circle around both end points of this side of the triangle. Select the radius larger than the estimated half of the triangle side.
5. The two circular lines meet at one point each above and below the side of the triangle.
6. Connect the two intersection points with the ruler.
7. This connecting line (called the vertical line) meets the side of the triangle at one point. This is the center of the triangle side.
8. Now connect this constructed center point with the opposite corner of the triangle with the ruler. You get the bisector.