G.1 Students understand the relationship between geometric ideas and their representation.
G.1.1 Demonstrate understanding by identifying and giving examples of undefined terms, axioms, theorems, and inductive and deductive reasoning;
G.1.2 Construct congruent segments and angles, angle bisectors, and parallel and perpendicular lines using a straight edge and compass, explaining and justifying the process used. Example: Construct the perpendicular bisector of a given line segment, justifying each step of the process.
G.2 Students identify and describe various kinds of triangles (right, acute, scalene, isosceles, etc.) They prove that triangles are congruent or similar and use properties of these triangles to solve problems.
G.2.1 Identify necessary and sufficient conditions for congruence and similarity in triangles, and use these conditions in proofs;
G.3.3 Identify and determine the measure of central and inscribed angles and their associated minor and major arcs. Recognize and solve problems associated with radii, chords, and arcs within or on the same circle;
G.3.5 Determine and use measures of sides and of interior and exterior angles of triangles, quadrilaterals, and other polygons to classify figures, develop mathematical arguments about geometrical relationships, and solve problems.
G.4.2 Construct the results (using technology when appropriate), and interpret transformations of figures in the coordinate plane, e.g., translations, reflections, rotations, scale factors, and the results of successive transformations. Apply transformations to the solutions of problems;
G.5 Students convert between units of measures and use rates and scale factors to solve problems. They compute the perimeter, area, and volume of geometric objects. They investigate how perimeter, area, and volume are affected by changes of scale.
G.5.1 Determine the perimeter, circumference, and area of common geometric figures such as parallelograms, trapezoids, circles, and triangles;
G.5.5 Use different degrees of precision in measurement, explain the reason for using a certain degree of precision, and apply estimation strategies to obtain reasonable measurements with appropriate precision for a given purpose.
G.6 Students apply geometric skills to making conjectures, using axioms and theorems, understanding the converse and contra positive of a statement, constructing logical arguments, and writing geometric proofs.
G.6.1 Construct and judge the validity of a logical argument and give counterexamples to disprove a statement;