Plane Geometry - Bruce E. Shapiro

18 SECTION 4. COMMON COREAt all levels the standards stress both procedural skill and conceptual understanding.The state of California has rewritten its content standards interms of the common core. 2California Common Core Standards for High School Geometryˆ Congruence– Experiment with transformations in the plane– Understand congruence in terms of rigid motions– Prove geometric theorems– Make geometric constructionsˆ Similarity, Right Triangles, and Trigonometry– Understand similarity in terms of similarity transformations– Prove theorems involving similarity– Define trigonometric ratios and solve problems involving right triangles– Apply trigonometry to general trianglesˆ Circles– Understand and apply theorems about circles– Find arc lengths and areas of sectors of circlesˆ Expressing Geometric Properties with Equations– Translate between the geometric description and the equation for a conic section– Use coordinates to prove simple geometric theorems algebraicallyˆ Geometric Measurement and Dimension– Explain volume formulas and use them to solve problems– Visualize relationships between two-dimensional and three-dimensional objectsˆ Modeling with Geometry– Apply geometric concepts in modeling situationsWhat the standards – NCTM, California, or Common Core – do NOTspecify is how to develop these concepts. Whether one should follow anaxiomatic Euclidean development, or the logical framework established byHilbert, or start with the smaller sets of axioms developed by groups such asthe School Mathematics Study Group (SMSG), the University of ChicagoSchool Mathematics Group (UCSMG) is left up to the individual school(teacher, district, etc). As a teacher learning the advanced mathematicalcontent behind these standards, it is important for you to understand eachof these perspectives so that you will understand where the frameworkthat is actually in use in your eventual school placement fits into the “bigpicture.”2 See http://www.cde.ca.gov/be/st/ss/. More detail is given in the standard; the boxgiven here is just from the summary page.« CC BY-NC-ND 3.0. Revised: 18 Nov 2012