VIDEO: Constructing angles with a compass

The classic case where a angle is constructed with the compass is the bisector. The constructed angle is exactly half the size of the starting angle. However, you can also construct any angle with a compass without a starting angle.

How to draw the bisector

1. To construct the bisector with a pair of compasses, you first need two Straight lines a and b, which intersect at a point S. The angle between the two straight lines is halved here.
2. Now set your compass to a radius r that is smaller than the length of the shorter straight line. A 3 cm radius is usually a good length.
3. Now insert the compass into the intersection point S and draw a circle around this point.
4. Now insert the compass at the intersection of the straight line a with the circle drawn around S. Draw a circle with the radius r around this point as well.


Right angle - this is how you construct it

A right angle should be constructed, "correctly", so only with compasses ...

5. Then draw a circle with the radius r around the intersection of the straight line b with the circle around S with the compass. It is important that you use the same radius as in point 4.
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6. The circles from points 4 and 5 intersect at two points. One of these points is point S. Connect the two intersection points with a ruler to get the bisector.

How to construct an angle with a pair of compasses

These instructions show how you can construct an angle with a given degree (for example 35 ° as in the video) with the help of the cosine function.

1. Define a starting point A and draw a segment in any direction that ends at this point.
2. Now construct a line perpendicular to this line by using the compass to draw a circle, the radius of which is greater than half the line, around both endpoints of the line. Then connect the two intersection points of the circles and you get a straight line perpendicular to the line.
3. The intersection of the line with the vertical line is point B in the triangle that you need to construct the angle.
4. In order to construct your angle now, you need the cosine as an angle function, which is valid in a right triangle. It reads: cos (α) = adjacent / hypotenuse = A / H. Since you know the angle α and you can measure the adjacent cathetus between points A and B, you now have to change the formula according to the hypotenuse H. This gives you the following formula: H = A / cos (α).
5. Plug your values ​​for A and α into the formula and calculate H with the calculator the end. This gives you the length of the hypotenuse H.
6. Now draw a circle with the radius equal to the length of H around point A. The intersection of the vertical straight line with this circle corresponds to point C of the triangle.
7. Now connect point C to point A so that you get the hypotenuse H. The angle between the adjacent cathetus A and the hypotenuse H corresponds to your desired angle α.