### G.RL: Geometry: Reasoning & Logic

#### G.RL.1: Use appropriate tools and logic to evaluate mathematical arguments.

G.RL.1.1: Understand the use of 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.

### G.2D: Geometry: Two-Dimensional Shapes

#### G.2D.1: 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, such as two-column proofs, paragraph proofs, flow charts, or illustrations.

G.2D.1.1: Apply the properties of parallel and perpendicular lines, including properties of angles formed by a transversal, to solve real-world and mathematical problems and determine if two lines are parallel, using algebraic reasoning and proofs.

G.2D.1.2: Apply the properties of angles, including corresponding, exterior, interior, vertical, complementary, and supplementary angles to solve real-world and mathematical problems using algebraic reasoning and proofs.

G.2D.1.4: Apply the properties of special quadrilaterals (square, rectangle, trapezoid, isosceles trapezoid, rhombus, kite, parallelogram) and use them to solve real-world and mathematical problems involving angle measures and segment lengths using algebraic reasoning and proofs.

G.2D.1.5: Use coordinate geometry to represent and analyze line segments and polygons, including determining lengths, midpoints, and slopes of line segments.

G.2D.1.6: Apply the properties of polygons to solve real-world and mathematical problems involving perimeter and area (e.g., triangles, special quadrilaterals, regular polygons up to 12 sides, composite figures).

G.2D.1.8: Construct logical arguments to prove triangle congruence (SSS, SAS, ASA, AAS and HL) and triangle similarity (AA, SSS, SAS).

G.2D.1.9: Use numeric, graphic and algebraic representations of transformations in two dimensions, such as reflections, translations, dilations, and rotations about the origin by multiples of 90°, to solve problems involving figures on a coordinate plane and identify types of symmetry.

### G.3D: Geometry: Three-Dimensional Shapes

#### G.3D.1: Solve real-world and mathematical problems involving three-dimensional figures.

G.3D.1.1: Solve real-world and mathematical problems using the surface area and volume of prisms, cylinders, pyramids, cones, spheres, and composites of these figures. Use nets, measuring devices, or formulas as appropriate.

### G.C: Geometry: Circles

#### G.C.1: Solve real-world and mathematical problems using the properties of circles.

G.C.1.3: 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.1.4: Apply the distance and midpoint formula, where appropriate, to develop the equation of a circle in standard form.

### G.RT: Geometry: Right Triangle Trigonometry

#### G.RT.1: Develop and verify mathematical relationships of right triangles and trigonometric ratios to solve real-world and mathematical problems.

G.RT.1.4: Apply the trigonometric functions as ratios (sine, cosine, and tangent) to find side lengths in right triangles in real-world and mathematical problems.

Correlation last revised: 9/16/2020

This correlation lists the recommended Gizmos for this state's curriculum standards. Click any Gizmo title below for more information.