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A Tale of Three Intersecting Lines

Three lines that cross

Push one bamboo pole with your foot. The gap in the middle changes shape. Does it always stay a triangle?

Two lines cross. One corner.
Step 1 of 4
  1. Two lines cross. One corner.
  2. A third line cuts both. Three corners, one triangle.
  3. Two lines run parallel instead. One corner goes missing.
  4. All three lines pass through one spot. The three corners are one point.

Three lines, two ways to fail

Not always. Three lines cross in pairs. Each pair meets at one corner. The three corners make a triangle.

Two things can spoil the triangle. Two parallel lines never meet, so a corner is missing. Or all three lines pass through one spot. Then the three corners are one point.

Turn the third line. Find where the triangle disappears.

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This track

  1. 0 Start here
  2. 1 Three lines that cross
  3. 2 Named by its sides
  4. 3 Named by its angles
  5. 4 The three angles come to 180°
  6. 5 Two angles decide the third
  7. 6 The angle that leans out
  8. 7 Will these three close?
  9. 8 Longest side, widest corner
  10. 9 Direct road, roundabout road
  11. 10 The height from a corner
  12. 11 Two angles and the side between
  13. 12 Checkpoint: roads, altitudes and rays
  14. 13 The big picture
  15. 14 Track quiz

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