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A Tale of Three Intersecting Lines

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Three bamboo poles lie crossed on the ground. In the middle is a small three-sided gap. Nobody put it there. The crossing poles made it.

One triangle: three corners and three sides.

Part I, Chapter 7 of your book is about that gap. The chapter is A Tale of Three Intersecting Lines. Lines that intersect cross each other. A corner is where two sides meet. We also use corner for its angle.

What this track covers

  • Three lines that cross. When they make a triangle.
  • Named by its sides. How many lengths match.
  • Named by its angles. The widest corner decides.
  • The three angles. They add to 180°.
  • The one left over. Two corners decide the third.
  • The exterior angle. Make a side longer, past a corner.
  • Will these close? Can three lengths make a triangle? There is a test.
  • Longest side, widest corner. They are across from each other.
  • Direct road, roundabout road. Two sides add to more than the third. This limits the third side.
  • The height from a corner. This line is an altitude. It may fall outside.
  • Two angles and a side. The angles must add to under 180°.

Quick catch-up

  • Measuring an angle: a full turn is 360°.
  • Kinds of angles: under 90° is acute. 90° is right. Over 90° is obtuse.
  • The distance all the way round: add every edge.

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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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