Track quiz
Thirteen quick questions. Use the table if you get stuck.
| Idea | The check |
|---|---|
| Copy a corner | Same radius. Carry the gap. |
| The perpendicular bisector | Every point is the same distance from both ends. |
| Split a corner | Both marks must be at the same distance. |
| A parallel | Measure square across at two places. |
| Three lengths | Each length must be less than the other two added. |
| Two lengths, angle between | The angle must sit between the two lengths. |
| A tiling | No gaps and no overlaps. |
| The whole turn | Tile corners at one point add to 360°. |
| A square line | To draw a perpendicular, you need a segment on the line. Its perpendicular bisector must go through your point. On the line, make the point the middle of the segment. Off the line, pick ends that are equally far from it. |
| 60°, 30° and 15° | Two arcs of one span make an equilateral triangle. Its corner is 60°. Bisect a corner to halve it. Bisect 60° to get 30°. Bisect 30° to get 15°. |
| A hexagon | Draw a circle. Keep the compass at the radius. Step it round the circle. Six steps come back to the start. Join the six points. That is a regular hexagon. |
| The tangram | A tangram is a square cut into seven pieces. Two big triangles are 1/4 each. The medium triangle is 1/8. So are the little square and the slanted piece. Two small triangles are 1/16 each. The shares add to 1. |
| Tiling the whole floor | Use copies of one regular shape, edge to edge. They tile when whole corners fill 360°. Divide 360° by the corner. A whole number means they fit. Only the triangle, square and hexagon do. |
You carry the gap correctly. But the new arc has a bigger radius. Is the copy the same corner?
A point is 6 cm from A and 6 cm from B. Where does it lie?
Marks are 25 mm and 35 mm out on the two arms. You finish the construction. What do you get?
Two lines do not cross anywhere on your page. Are they parallel?
A shop has strips of 3 cm, 4 cm and 9 cm. Do the arcs meet?
A 40° corner is at the end of a 60 mm side. A 45 mm side sits across from it. How many triangles fit?
Can 2 × 1 tiles cover a 5 × 5 grid?
Three corners of 108° meet at a point. Do they fill it?
A point is 40 mm above a line. You strike an arc with the compass at 50 mm. How does the arc meet the line?
You start with 60°. You bisect it, then add 60°. What corner do you get?
A circle has a radius of 45 mm. You step a 45 mm span round it. How long is each side of the hexagon?
Which pieces together make exactly half of the tangram square?
Which regular shape, used alone, can never fill a point exactly?
Chapter 6 of Part II is Constructions and Tilings. Try its designs with a compass.
Next: Finding the Unknown. What an equals sign claims. How to work back to a hidden number.