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.

Biconditional Statements
Investigating Angle Theorems
Isosceles and Equilateral Triangles

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.

Biconditional Statements
Conditional Statements

G.RL.1.3: Assess the validity of a logical argument and give counterexamples to disprove a statement.

Biconditional Statements
Conditional Statements

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.

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Parallel, Intersecting, and Skew Lines
Triangle Angle Sum

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.

Congruence in Right Triangles
Proving Triangles Congruent

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.

Classifying Quadrilaterals
Parallelogram Conditions
Special Parallelograms

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

Point-Slope Form of a Line

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).

Perimeter and Area of Rectangles
Perimeters and Areas of Similar Figures

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

Congruence in Right Triangles
Proving Triangles Congruent

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.

Dilations
Rotations, Reflections, and Translations
Translations

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.

Prisms and Cylinders
Pyramids and Cones
Surface and Lateral Areas of Prisms and Cylinders
Surface and Lateral Areas of Pyramids and Cones

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.

Circles

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

Circles

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.

Cosine Function
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function