Geometry Mathematics

Oklahoma Academic Standards · 2022

  • Reasoning & Logic (G.RL)

    • G.RL.1

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

      • G.RL.1.1

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

      • G.RL.1.2

        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

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

  • Two-Dimensional Shapes (G.2D)

    • G.2D.13

      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.1.16

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

      • G.2D.1.2

        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.1.36

        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

        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

        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

        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.1.76

        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

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

      • G.2D.1.98

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

      • G.2D.1.10

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

      • G.2D.1.11

        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.

  • Three-Dimensional Shapes (G.3D)

    • G.3D.13

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

      • G.3D.1.15

        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

        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.

  • Circles (G.C)

    • G.C.15

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

      • G.C.1.1

        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.1.26

        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.1.36

        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.

  • Right Triangle Trigonometry (G.RT)

    • G.RT.15

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

      • G.RT.1.18

        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

        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

        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.1.43

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