is the part of mathematics that covers the properties, measurement and relationships between points, lines, angles, shapes and objects.

The last six topics were all part of geometry.






Key things to know

Points are usually named using CAPITAL letters.
The three points P, Q and R.

Lines are usually named using any two points lying on the line.

Each point is named using a capital letter.

The line PQ.

Parts of lines are called line segments or intervals.

These are named using capital letters at each end of the line.

The interval or line segment AB.

The ways of naming angles are given in Unit 30.

There are several mathematical instruments that are very useful for studying geometry:

The ruler

A ruler can be used to:

  • Draw shapes such as triangles and rectangles.
  • Join points with straight lines
  • Measure lengths of lines

Most rulers allow measurements to be made to the nearest millimetre, which is one tenth of a centimetre.

Using a ruler

To draw a line between two points and measure its length

To draw a line between P and Q and measure its length Line up ruler with 0 cm on point P and move other end of ruler to point Q Draw line from P to Q and use scale on ruler to read off the length of PQ.

The protractor

A protractor can be used to measure the size of an angle.


Although the first protractor shown above has a scale that only goes from 0o to 180o both of the protractors shown can be used to measure angles of any size.

Using a protractor

To measure the size of an angle.

To measure the angle ABC. Move protractor so that the middle point of the protractor is on the vertex or corner of the angle. One of the arms of the angle should line up with the bottom (zero) line of the protractor.

Read the size of the angle of the scale.

In this case it will be top number.


The set square

Set squares are instruments used for drawing angles of 30, 45 or 60 degrees and for constructing parallel and perpendicular lines.

There are two basic types of set squares

With angles of 45o
With angles of 30o and 60o

Using a set square

To construct perpendicular and parallel lines.

To draw a perpendicular line at R
Two parallel lines AB and CD

The compasses

Compasses (often called a "pair of compasses" or a "compass") is an instrument used for drawing circles and arcs of circles. Compasses have two arms which are joined together. One arm has a pin to mark the centre of the arc or circle and the other arm holds a pencil or pencil lead.

This is a completeley different instrument from a navigational compass which is used to find the direction of north.


Using compasses

To draw circles
To draw arcs