Geometry
Shapes can be measured with a ruler. How do you know a fact about a shape holds for every one of its kind, even the ones nobody has drawn?
Where you are 11 inside
What this area is about
Geometry studies shapes and space: what figures are, how they move, how big they are, and the reasoning that proves facts about them. It runs from naming a triangle in kindergarten to proofs, equations of curves and solids in high school.
How these fit together
Starting objects. Points, lines and planes starts from those three undefined terms and builds segments, angles and parallel lines from them. Two-dimensional shapes names and sorts flat figures.
Figures. Triangles carry most of plane geometry’s theorems. Circles add arcs, tangents and their angle facts. Solids take shapes into three dimensions, with surface area and volume.
Motions and matching. Transformations slide, flip and turn figures without changing lengths or angles. Similarity adds scaling by a factor k > 0.
Methods. Coordinate geometry computes with (x, y). Geometric proof argues from definitions to conclusions that hold for every figure. Constructions draw exactly with compass and straightedge.
Beyond. Conic sections are the curves a plane cuts from a double cone when it misses the vertex: circle, ellipse, parabola or hyperbola.
A path through it
These areas interleave rather than stack. Points, lines and planes and the first flat shapes come first. Then coordinate geometry and triangles, which draw on each other, and transformations; the regular-polygon lessons in two-dimensional shapes wait for transformations. Then circles, solids and similarity, in that order. Last geometric proof, then constructions; conic sections also come late, after circles and solids.
Next: trigonometry, angles and triangles and then the waves they turn into.