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Triangle - construction

A triangle can be constructed with a compass, a ruler and a protractor. You also need some squared paper and a pencil.

Triangle drawing machine

Our drawing machine can construct a triangle with a compass, a ruler and a protractor if at least three pieces of information about the triangle are given. At the same time the machine will tell you how the construction of the triangle is carried out.

Construct a triangle with compass, ruler and protractor

Angles Side lengths
A: |AB|:
B: |AC|:
C: |BC|:

How to construct a triangle?

ABC triangle with side lengths
At first you need an overview of the information about the triangle you have.

A good place to start is by drawing the base line, which is the basis of the further construction of the triangle.

In the following explanations are the vertices of a triangle called A, B and C, and the side lengths are called |AB|, |AC| and |BC|. We will explain how the construction of the triangle is carried out, depending on which of the mentioned information that are given.

Not all possible situations are explained, but hopefully it’s enough to give you an idea of what to do, when the triangle's information is presented to you.

And remember, you can always use the drawing machine above, if you need help.



If all the side lengths are given:

First you draw the base line |AB|.
Then you set your compass to the length |AC|, put the needle point in the point A and draw a circle.
Then you set your compass to the length |BC|, put the needle point in the point B and draw a circle.
In the point of intersection between the two circles, you’ll find the point C. The triangle is complete when you connect all three points with straight lines.



If the side length |AB|, the angle A and the side length |AC| is given:

First you draw the line |AB|. You put your protractor in the point A and measure the angle A from the line |AB|. You mark the angle with a small dot.
Then you draw a straight line passing through A and the small dot.
On this line you measure the length |AC|, and you will get the point C.
You can now connet B and C with a straight line.



If the length |AC|, the angle A and the angle C is given:

First you draw the line |AC|.
Then you measure the angle A and put a small mark.
You draw a straight line passing through A and the small dot.
You do the same with the angle C.
In the point of intersection between the two lines, you’ll find the point B, and you can complete the triangle.



If the length |AC|, the angle A and the angle B is given:

First you calculate the angle C. It's possible, because you know that the angle sum of a triangle is 180˚. The angle C is therefor given by C = 180-A-B.
Now you have the length |AC|, the angle A and the angle C, and that is exactly the same as in the example above.

How to use a protractor

The protractor has a base line passing through 0˚ and 180˚.

The base line is placed on the line from which, you want to measure the angle, with the midpoint of the base line placed in the vertex where the angle is. Then you can find the angle on the scale and put a mark there.

You can now remove the protractor an draw a straight line from the vertex to the mark.

How to use a compass?

First you loosen the compass and put the part with the spike at 0 on a ruler.
Then you adjust the compass to the desired length by moving the part with the pencil and lock it in its position.
You can now place the spike in the desired center point, and when you turn the compass around, you’ll get a circle.