For many high school students, geometry is the first experience with proof problems. Since geometry relies heavily upon proofs, and proofs rely heavily upon mathematical logic, it is often most suitable to begin a geometry course with the teaching of proof and logic techniques. The introduction of logic and proofs should take around 4 weeks.
Since algebra tends to be a prerequisite for geometry, new geometry students are usually already well-versed in the basics of lines. However, you should introduce new topics, such as the ideas of how lines and planes relate, parallelism, as well as the ideas of lines from angles and how to measure angles. This topic should take around 5 weeks.
Trigonometry plays an integral role in geometry. It takes a significant amount of time to cover concepts; such as the comparisons of triangles, triangle proof methods and the implications of the relationships between the sides and angles of right triangles -- square roots, trigonometric functions, and so on. This section should take approximately 9 weeks.
In geometry teaching, it is standard to move from triangles to shapes with more sides. Polygons as a subject, covers all of the familiar and commonly met shapes in geometry, including quadrilaterals and n-gons. This topic, though covering many shapes, does not need much time, as many of the theorems for n-gons are simple enough to apply to quadrilaterals. This section should take around 4 weeks.
Geometry teachers tend to teach circles as the final shape in geometry because of their complexity. Although only one shape, circles tend to require around 3 weeks to cover completely.
Commonly, the final subject of geometry is the manipulation of shapes. This topic includes translations, rotations, reflections, tessellations and patterns. This diverse topic usually requires 5 weeks to complete.