Basic geometry

Geometry is about studying and working with shapes, lines, points, angles and surfaces.  Some of the simple stuff is very easy to understand, but as you learn more about it there is some fairly hard material to cover.  We can start with the really simple stuff and build it up from there.


Working with angles is different to working with something like length.  The length of something tells you how far it is from one end to the other end:

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Angles on the other hand tell you how much you have to turn or rotate to change from one direction to another.  For instance, if you have two lines pointing in different directions, the angle between those two lines tells you how much you need to turn to change from one line to the other.  Angles are usually shown using a slightly curved line drawn between the two lines:

So what do we measure angles in?  We already measure things like length in metres or millimetres or kilometres.  Well, angles can be measured using units called degrees’.  The symbol for degrees is a little circle – ‘°’.  It is written above and to the right of the number. So how much is a degree?  Well, you can get a feel for what a degree is using the following diagrams:

When you rotate or turn from a horizontal line to a vertical line, the angle is 90 degrees.

When you rotate all the way from facing one way to facing in the opposite direction, the angle is 180 degrees.

When you rotate even more than this, like in the diagram, the angle is 270 degrees.

When you rotate all the way around until you’re pointing the direction you started, the angle is 360 degrees.  When you rotate through 360 degrees, people often call it one complete rotation”.