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Constructions and Tilings

A parallel through a point

Check the gap between two window bars. It is the same at the top and the bottom.

The first line, and a point P above it.
Step 1 of 5
  1. The first line, and a point P above it.
  2. Rule a slanted line from P down to the first line, at Q.
  3. Strike an arc at Q. It leaves two marks.
  4. Copy that corner at P. Rule the new line through P.
  5. Measure square across (at 90° to the lines) at two places. The gaps match.

Copy the corner, carry the line

Rule a slanted line from P to the first line. Call the crossing Q. Copy the corner at Q onto the slanted line at P. The new arm points the same way as the first line.

Equal matching corners make the two lines parallel. Parallel lines keep the same gap.

Watch out!

Not meeting on your page does not prove parallel. Measure square across at two places.

Slip the compass. Watch the two gaps.

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This track

  1. 0 Start here
  2. 1 Copy a corner, no protractor
  3. 2 The line fair to both ends
  4. 3 Split a corner in two
  5. 4 A parallel through a point
  6. 5 Three lengths, one triangle
  7. 6 Two sides, the angle between
  8. 7 Covering a floor with no gaps
  9. 8 The corners must add to 360°
  10. 9 A square line from a point
  11. 10 60°, 30° and 15° with a compass
  12. 11 A hexagon from a circle
  13. 12 The tangram
  14. 13 Tiling the whole floor
  15. 14 Checkpoint: perpendiculars, 60°, hexagons and floors
  16. 15 The big picture
  17. 16 Track quiz

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