Points, lines and planes
Geometry has to start somewhere. What do you take for granted, and what can you build from it?
Where you are 8 inside
What this area is about
Every definition uses other words, so a chain of definitions has to stop somewhere. School geometry stops at three: point, line and plane. They are not defined, only described, and every other figure is built from them.
How these fit together
The starting objects. Points, lines and planes explains why the three are left undefined and what is assumed instead, and names collinear and coplanar points, which share a line or a plane.
How they sit together. Lines and planes in space says what lines and planes can share: two different lines meet in at most one point, and two different planes that meet do so in a line. It also holds skew lines, which only exist in three dimensions, and space, the setting for solids.
Built pieces. Segments, rays and length are pieces of a line, and give length. Angles and how to name them: two rays from one point, giving turn. Locus of points: a figure described by a condition rather than drawn.
The first results. Angle types and pairs and parallel lines and transversals are where these objects start forcing facts about each other.
A path through it
Points, lines and planes, then intersections in space. Then angles, and angle types and pairs before segments and rays, whose perpendicular bisector needs perpendicular lines. Then parallel lines and a locus. Skew lines and figures in space can wait for solids.
This is the ground floor: triangles and everything after are built from these pieces.