Geometry

Use appropriate tools and logic, including algebraic methods, to evaluate mathematical arguments.

• G.RL.1.1(Objective)

  Use undefined terms, definitions, postulates, and theorems in logical arguments/proofs.

• G.RL.1.2(Objective)

  Analyze and draw conclusions based on a set of conditions using inductive and deductive reasoning. Recognize the logical relationships between a conditional statement and its inverse, converse, and contrapositive.

• G.RL.1.3(Objective)

  Assess the validity of a logical argument and give counterexamples to disprove a statement.

Discover, evaluate, and analyze the relationships between lines, angles, and polygons to solve real-world and mathematical problems; express proofs in a form that clearly justifies the reasoning (e.g., two-column proofs, paragraph proofs, flowcharts).

• G.2D.1.1(Objective)

  Use properties of parallel lines cut by a transversal to determine angle relationships and solve problems.

• G.2D.1.2(Objective)

  Use the angle relationships formed by lines cut by a transversal to determine if the lines are parallel and verify, using algebraic and deductive proofs.

• G.2D.1.3(Objective)

  Apply the properties of angles (corresponding, exterior, interior, vertical, complementary, supplementary) to solve problems using mathematical models, algebraic reasoning, and proofs.

• G.2D.1.4(Objective)

  Apply theorems involving the interior and exterior angle sums of polygons to solve problems using mathematical models, algebraic reasoning, and proofs.

• G.2D.1.5(Objective)

  Apply the properties of special quadrilaterals (square, rectangle, trapezoid, isosceles trapezoid, rhombus, kite, parallelogram) to solve problems involving angle measures and segment lengths using mathematical models, algebraic reasoning, and proofs.

• G.2D.1.6(Objective)

  Use coordinate geometry and algebraic reasoning to represent and analyze line segments and polygons, including determining lengths, midpoints, and slopes of line segments.

• G.2D.1.7(Objective)

  Apply the properties of polygons, and use them to represent and apply mathematical models involving perimeter and area (e.g., triangles, special quadrilaterals, regular polygons up to 12 sides, composite figures).

• G.2D.1.8(Objective)

  Apply the properties of congruent or similar polygons to solve problems using mathematical models and algebraic and logical reasoning.

• G.2D.1.9(Objective)

  Construct logical arguments to prove triangle congruence (SSS, SAS, ASA, AAS, and HL).

• G.2D.1.10(Objective)

  Construct logical arguments to prove triangle similarity (AA, SSS, SAS).

• G.2D.1.11(Objective)

  Use numeric, graphic, and algebraic representations of transformations in two dimensions (e.g., reflections, translations, dilations, rotations about the origin by multiples of 90°) to solve problems involving figures on a coordinate plane and identify types of symmetry.

Solve real-world and mathematical problems involving three-dimensional figures.

• G.3D.1.1(Objective)

  Represent, use, and apply mathematical models and other tools (e.g., nets, measuring devices, formulas) to solve problems involving surface area and volume of three-dimensional figures (prisms, cylinders, pyramids, cones, spheres, composites of these figures).

• G.3D.1.2(Objective)

  Use ratios derived from similar three-dimensional figures to make conjectures, generalize, and to solve for unknown values such as angles, side lengths, perimeter, and circumference of a face, area of a face, and volume.

Solve real-world and mathematical problems using the properties of circles.

• G.C.1.1(Objective)

  Apply the properties of circles to solve problems involving circumference and area, using approximate values and in terms of pi, using algebraic and logical reasoning.

• G.C.1.2(Objective)

  Use the distance and midpoint formula, where appropriate, to recognize and write the radius r, center (h,k), and standard form of the equation of a circle (x − h)² + (y − k)² = r² with and without graphs.

• G.C.1.3(Objective)

  Apply the properties of circles and relationships among angles; arcs; and distances in a circle among radii, chords, secants, and tangents to solve problems using algebraic and logical reasoning.

Apply mathematical relationships of right triangles and trigonometric ratios to solve real-world and mathematical problems.

• G.RT.1.1(Objective)

  Apply the distance formula, the Pythagorean theorem, and the Pythagorean theorem converse (approximate and exact values, including Pythagorean triples) to solve problems, using algebraic and logical reasoning and mathematical models.

• G.RT.1.2(Objective)

  Verify and apply properties of right triangles, including properties of 45-45-90 and 30-60-90 triangles, to solve problems using algebraic and logical reasoning.

• G.RT.1.3(Objective)

  Use the definition of the trigonometric functions to determine the sine, cosine, and tangent ratio of an acute angle in a right triangle. Apply the inverse trigonometric functions to find the measure of an acute angle in right triangles.

• G.RT.1.4(Objective)

  Apply the trigonometric functions as ratios (sine, cosine, tangent) to find side lengths in right triangles in mathematical models, including the coordinate plane.