Ruler-and-compass constructions
Use compasses (pair of compasses) and a ruler to meet chords and arcs, construct a perpendicular bisector and an angle bisector, and build triangles from their sides.
- UK: Year 6
- France: grade 2
- Germany: grade 3
- Iran: grade 10
- Afghanistan: grade 4
- Syria: grade 5
- Palestine: grade 6
- Ukraine: grade 2
- Russia: grade 4
Guide
This studio is for Year 6 and up (KS3 constructions; Afghan Grade 6 «ترسیمات هندسی»; Iran's Grade 10 geometry).
The compasses (pair of compasses) tool: tap Compasses, then the centre, then a point the circle should pass through. Wherever two circles, or a circle and a line, cross, a new point appears that the pencil snaps to. Tap Pencil to draw lines again.
In every task the point you need is not one of the board's dots, so you can only reach it by constructing it, not by eye.
Why do the constructions work? Every point on the perpendicular bisector is the same distance from both ends of the segment, and two equal circles drawn from the ends cross exactly at such points. In the equilateral triangle, both radii are the side itself, so all three sides come out equal.