#### G.1: Logical arguments and proofs

G.1.D: Write the converse, inverse, and contrapositive of a valid proposition and determine their validity.

#### G.2: Lines and Angles

G.2.B: Know, prove, and apply theorems about angles, including angles that arise from parallel lines intersected by a transversal

G.2.C: Explain and perform basic compass and straightedge constructions related to parallel and perpendicular lines.

G.2.D: Describe the intersections of lines in the plane and in space, of lines and planes, and of planes in space.

#### G.3: Two- and three-dimensional figures

G.3.A: Know, explain, and apply basic postulates and theorems about triangles and the special lines, line segments, and rays associated with a triangle.

G.3.B: Determine and prove triangle congruence, triangle similarity, and other properties of triangles.

G.3.C: Use the properties of special right triangles (30°-60°-90° and 45°-45°-90°) to solve problems.

G.3.D: Know, prove, and apply the Pythagorean Theorem and its converse.

G.3.E: Solve problems involving the basic trigonometric ratios of sine, cosine, and tangent.

G.3.F: Know, prove, and apply basic theorems about parallelograms.

G.3.G: Know, prove, and apply theorems about properties of quadrilaterals and other polygons.

G.3.H: Know, prove, and apply basic theorems relating circles to tangents, chords, radii, secants, and inscribed angles.

G.3.J: Describe prisms, pyramids, parallelepipeds, tetrahedra, and regular polyhedra in terms of their faces, edges, vertices, and properties.

#### G.4: Geometry in the coordinate plane

G.4.A: Determine the equation of a line in the coordinate plane that is described geometrically, including a line through two given points, a line through a given point parallel to a given line, and a line through a given point perpendicular to a given line.

G.4.D: Determine the equation of a circle that is described geometrically in the coordinate plane and, given equations for a circle and a line, determine the coordinates of their intersection(s).

#### G.5: Geometric transformations

G.5.A: Sketch results of transformations and compositions of transformations for a given two-dimensional figure on the coordinate plane, and describe the rule(s) for performing translations or for performing reflections about the coordinate axes or the line y = x.

G.5.B: Determine and apply properties of transformations.

G.5.D: Describe the symmetries of two-dimensional figures and describe transformations, including reflections across a line and rotations about a point.