Chapter 1 of seven · Geometry & Algebra
Foundations
What we agree on, angles, and the first letters. Meets at distributivity as a rectangle.
- Point, line, ray, and segmentThe handful of starting words every later lesson leans on, and how to check whether a point really sits between two others.
- Angle as an amount of turningWhat an angle is, what a degree measures, and why the vertex and the arm lengths do not matter.
- The postulates, stated plainly, including the parallel postulateWhat a postulate is, why some things must be agreed rather than proved, and Playfair's form of the parallel postulate.
- Angles on a straight line sum to 180Splitting a straight angle in two, and why the two parts always add back up to a straight angle.
- Angles at a point sum to 360Splitting a full turn in four, and why the pieces always add back up to 360.
- Vertically opposite angles are equalTwo crossing lines make two matching pairs of angles, and here is why.