Geometry
Basic geometrical ideas
Tell points, lines, rays and line segments apart, name the parts of an angle and a circle, and count the sides and diagonals of a polygon.
Geometry starts with a point: a position, with no size at all. Join two points and you have a line segment, which has two ends and a length you can measure. Let one end run on for ever and it becomes a ray. Let both ends run on and it becomes a line, which has no ends and no length — which is why every straight thing you can actually measure is a segment.
The parts of an angle
An angle is made where two rays start from the same point. Those rays are its arms, and the point they share is its vertex. How long you draw the arms makes no difference to the angle — only the amount of turn between them counts.
Have a play
Three lines are drawn on this circle. Take them in turn and find out what each one is called, looking at where each one starts and where it ends.
Tap any part of the picture.
Worked example
How many line segments can be drawn joining pairs of four points, when no three of them lie on one straight line?
Take the first point. It can be joined to each of the other three, so that is 3 segments.
A segment needs two points, and one of them is fixed for now.
Try it together
Now let us count the diagonals of a pentagon.
Same method as the example: count the joins, halve for double counting, then take away the ones that are sides rather than diagonals.
1.Each corner of a pentagon can be joined to how many other corners?
Have a go
Have a go on your own: how many sides does an octagon have?
Hint: The same number as its corners.
Ready to practice?
Eight questions on what you have just read. Nothing is timed, and you can play as many times as you like.