Students bring many geometric experiences with them to high school; in this course, they begin to use more precise definitions and develop careful proofs. Although there are many types of geometry, this course focuses on Euclidean geometry, studied both with and without coordinates. This course begins with an early definition of congruence and similarity with respect to transformations, then moves on through the triangle congruence criteria and other theorems regarding triangles, quadrilaterals and other geometric figures. Students then move on to right triangle trigonometry and the Pythagorean theorem, which they may extend to the Laws of Sines and Cosines (+). An important aspect of the Geometry course is the connection of algebra and geometry when students begin to investigate analytic geometry in the coordinate plane. In addition, students in Geometry work with probability concepts, extending and formalizing their initial work in middle school. They compute probabilities, drawing on area models. Area models for probability can serve to connect this material to the other aims of the course.
To summarize, high school Geometry corresponds closely to the Geometry conceptual category in the high school standards. Thus, the course involves working with congruence (G-CO), similarity (G-SRT), right triangle trigonometry (in G-SRG), geometry of circles (G-C), analytic geometry in the coordinate plane (G-GPE), and geometric measurement (G-GMD) and modeling (G-MG). The Standards for Mathematical Practice apply throughout the Geometry course and, when connected meaningfully with the content standards, allow for students to experience mathematics as a coherent, useful and logical subject. Details about the content and practice standards follow in this analysis.