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Constructions and Tilings

Two sides, the angle between

Two roads leave a junction, a place where roads meet. A straight footpath joins them.

The first side, L to R.
Step 1 of 4
  1. The first side, L to R.
  2. Open the corner at L to the size given.
  3. Step the second length along that arm.
  4. Join the end back to R.

A second method

Rule the first side, L to R. Draw the corner at L to the size given. Mark the second length along the new arm. Call the end D. Join D to R.

Two lengths and the angle between them decide the third side. You never chose it, so measure it.

Example: sides 6 cm and 3 cm, with a 50° corner between. One triangle fits.

Watch out!

The corner must sit between the two lengths. Take a 60 mm side with a 40° corner at one end. A 45 mm side sits across from that corner. Two triangles fit.

Slide the corner. Flip the switch to move the corner. Watch the third side.

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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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