# Mathematics, Standard C: Geometry Performance Standards - Grade 12

By the end of grade twelve, students will:

C.12.1 Identify, describe, and analyze properties of figures, relationships among figures, and relationships among their parts by

• constructing physical models
• drawing precisely with paper-and-pencil, hand calculators, and computer software
• using appropriate transformations* (e.g., translations, rotations, reflections, enlargements)
• using reason and logic

C.12.2 Use geometric models* to solve mathematical and real-world problems

C.12.3 Present convincing arguments by means of demonstration, informal proof, counter-examples, or any other logical means to show the truth of

• statements (e.g., these two triangles are not congruent)
• generalizations (e.g., the Pythagorean* theorem holds for all right triangles)

C.12.4 Use the two-dimensional rectangular coordinate system* and algebraic procedures to describe and characterize geometric properties and relationships such as slope*, intercepts*, parallelism, and perpendicularity

C.12.5 Identify and demonstrate an understanding of the three ratios used in right-triangle trigonometry (sine, cosine, tangent)

*See Glossary.