There are points and lines.

• 2 points determine a unique line, two lines are either parallel or determine a unique point which is in both lines. If the lines are parallel they have no point in common.
• Line segments, directed line segments, rays, angles triangles, are defined in the usual ways.
• There is a measure of length that:
  •   Is additive on every line: the length of two disjoint or adjacent segments is the sum of their lengths.
  •   Obeys the triangle inequality ( any one side is shorter than the sum of the lengths of the other two).
• There is an additive measure of angle: so that the size of the sum of two angles is the sum of their sizes.
• Rays or line segments that make half of a flat (flat means a 180 degree angle) are normal ,  perpendicular and orthogonal to one another.