Level 2 · Ages 8–11
Read it again any time, including while you work through the exercises.
Welcome to the geometer's workshop! Everything starts with a point: a tiny mark showing an exact spot. We name it with a capital letter, like point A or point B. Then two points are enough to build everything else.
If you join A and B with your ruler, stopping exactly at both points, you draw a segment. We write it [AB] with square brackets, like little gates saying: stop, it ends here! If instead your line goes through A and B and continues forever on both sides, it is a line, written (AB) with round brackets.
When several points sit on the same line, we say they are aligned, like beads on a tight string.
And the circle? Take a compass: the needle sits at the centre, and the pencil traces all the points located at exactly the same distance from the centre. This distance is called the radius. If you cross the circle from edge to edge through the centre, you get the diameter: it measures twice the radius. Remember the magic formula: diameter = 2 × radius.
The radius of a circle is 3 cm. How long is its diameter?
diamètre = 2 × rayon
The diameter crosses the circle through the centre: it is like two radii placed end to end.
2 × 3 = 6
I multiply the radius by 2: 2 times 3 cm makes 6 cm.
Result: The diameter is 6 cm.
You are given [AB], (AB) and point A. Which is which?
A
A capital letter alone names a point: an exact spot, with no length.
[AB]
Square brackets are gates: [AB] is the segment from A to B, stopping at both ends. You can measure it!
(AB)
Round brackets are open: (AB) is the line through A and B, running forever both ways. Impossible to measure.
Result: A is a point, [AB] a segment (measurable), (AB) a line (infinite).