Introduction

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

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.

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 connect 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 therefore 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.

Construct an Isosceles Triangle Using Given Segment Lengths:

When constructing an isosceles triangle, you may be given pre-determined segment lengths to use for the triangle (such as in this example), or you may be allowed to determine your own segment lengths.  Either way, the construction process will be the same.

Construct an isosceles triangle whose legs and base are of the pre-determined lengths given.  Construct the new triangle on the reference line.

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SS1 Mathematics Third Term: Content Geometrical Construction