Use a compass and a ruler the way mathematicians do. Pick the next step and watch exact geometry appear: circles, middles, equal angles and perfect triangles.
Start here. A construction is a drawing made with only two tools: a ruler (to draw straight lines) and a compass (to draw circles and arcs). You do not measure angles. You make them exact by using circles.
How a compass works. The compass has a sharp point and a pencil. The point stays still on the centre. The pencil swings round and draws every spot that is the same distance from the centre. That distance is the radius, and the compass opening remembers it. An arc is just a piece of a circle.
The big secret. Every point on a circle is the same distance from its centre. When two arcs with the same opening cross, the crossing point is the same distance from both centres. That is why the crossing points land in exactly the right place.
Cutting a line in half. Draw arcs from both ends of a segment with the same opening, wider than half the segment. The two crossings are both the same distance from each end. The line through them cuts the segment in half, at a right angle. It is called the perpendicular bisector.
Cutting an angle in half. Draw an arc from the corner so it crosses both arms. Then draw two arcs with the same opening from those crossings. The line from the corner through where they meet splits the angle into two equal angles. It is called the angle bisector.
Perfect shapes. Keep the same opening and the sides come out equal. That gives an equilateral triangle (three equal sides, three 60° angles) and a regular hexagon, because the radius of a circle fits exactly six times round its edge.
Try this above. In Play, step through each drawing and watch the new part glow gold. In Missions, choose the next step yourself. In Build It, put the steps in order while a faint picture shows the goal.
A construction is a drawing made with a compass and an unmarked ruler only. The ancient Greeks loved them because every line and angle can be explained and proved. You never need a protractor or a measured number.
No. The game draws the exact lines for you when you pick the right step. If you have a real compass, you can copy each drawing on paper to feel how it works.
The opening is the radius. If it changes, the arcs no longer meet at points that are equally far from both centres, and the middle or the angle will be wrong. Keeping the opening the same is what makes the construction exact.
Pick the level, not the age. "Just starting" draws circles and copies lengths. "I know the basics" bisects lines and angles and copies an angle. "Challenge me" builds perpendiculars, a 60° angle, equilateral triangles and a hexagon.
No. It is free and needs no account. Your stars are saved in your own browser.