A ruler and a pair of compasses are really important equipment for a geometer. Indeed, for more hat a thousand years **constructions** using these two tools were at the heart of what mathematics was. The most important mathematics textbook of all time (Euclid’s “Elements”) is a series of increasingly difficult constructions over 13 books.

When we use the ruler and pair of compasses, we must take care to be accurate. Once we have **set the compass**, it’s best only to touch the top part lightly, to stop it from changing.

**Exercise**

Let’s get some practice in using our pairs of compasses, by constructing the circles and other shapes detailed in exercise 3A on pages 36 and 37 of the textbook:

**Triangles**

If we know the lengths of each of the sides of a triangle, we can draw the triangle using a ruler and a pair of compasses. You must always use the pair of compasses and not try to do it just with the ruler, as if you do that the angles of the triangle will not be accurate.

Let’s watch the teacher demonstrate how the compasses help us do this.

**Exercise**

Let’s complete question 1 from exercise 3B on page 39:

Do we remember the name of the long side on a right-angled triangle?

We have a special method that we use if we want to draw a right-angled triangle. We start by drawing one side length and then we **construct a perpendicular line** at one extreme of it. Then we check which side lengths we know and use our pencil and pair of compasses to complete the triangle.

**Exercise**

Let’s complete question 2 from exercise 3B on page 39: