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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.

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.