G.1: Geometric Properties and Reasoning

G.1.1: Properties of Circles, Spheres, and Cylinders

G.1.1.1: Identify and/or use parts of circles and segments associated with circles, spheres, and cylinders.

G.1.1.1.1: Identify, determine, and/or use the radius, diameter, segment, and/or tangent of a circle.

Chords and Arcs
Circumference and Area of Circles
Inscribed Angles

G.1.1.1.2: Identify, determine, and/or use the arcs, semicircles, sectors, and/or angles of a circle.

Chords and Arcs
Inscribed Angles

G.1.1.1.3: Use chords, tangents, and secants to find missing arc measures or missing segment measures.

Chords and Arcs

G.1.1.1.4: Identify and/or use the properties of a sphere or cylinder.

Prisms and Cylinders
Surface and Lateral Areas of Prisms and Cylinders

G.1.2: Properties of Polygons and Polyhedra

G.1.2.1: Recognize and/or apply properties of angles, polygons, and polyhedra.

G.1.2.1.1: Identify and/or use properties of triangles.

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Triangle Inequalities

G.1.2.1.2: Identify and/or use properties of quadrilaterals.

Classifying Quadrilaterals
Parallelogram Conditions
Special Parallelograms

G.1.2.1.3: Identify and/or use properties of isosceles and equilateral triangles.

Classifying Triangles
Concurrent Lines, Medians, and Altitudes
Isosceles and Equilateral Triangles
Triangle Inequalities

G.1.2.1.4: Identify and/or use properties of regular polygons.

Polygon Angle Sum

G.1.2.1.5: Identify and/or use properties of pyramids and prisms.

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

G.1.3: Congruence, Similarity, and Proofs

G.1.3.1: Use properties of congruence, correspondence, and similarity in problem-solving settings involving two- and three-dimensional figures.

G.1.3.1.1: Identify and/or use properties of congruent and similar polygons or solids.

Perimeters and Areas of Similar Figures
Proving Triangles Congruent
Similar Figures
Similarity in Right Triangles

G.1.3.1.2: Identify and/or use proportional relationships in similar figures.

Perimeters and Areas of Similar Figures
Similarity in Right Triangles

G.1.3.2: Write formal proofs and/or use logic statements to construct or validate arguments.

G.1.3.2.1: Write, analyze, complete, or identify formal proofs (e.g., direct and/or indirect proofs/proofs by contradiction).

Investigating Angle Theorems
Isosceles and Equilateral Triangles
Pythagorean Theorem

G.2: Coordinate Geometry and Measurement

G.2.1: Coordinate Geometry and Right Triangles

G.2.1.1: Solve problems involving right triangles.

G.2.1.1.1: Use the Pythagorean theorem to write and/or solve problems involving right triangles.

Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function

G.2.1.1.2: Use trigonometric ratios to write and/or solve problems involving right triangles.

Sine, Cosine, and Tangent Ratios

G.2.1.2: Solve problems using analytic geometry.

G.2.1.2.1: Calculate the distance and/or midpoint between two points on a number line or on a coordinate plane.

Circles
Distance Formula
Points in the Coordinate Plane

G.2.1.2.2: Relate slope to perpendicularity and/or parallelism (limit to linear algebraic equations).

Cat and Mouse (Modeling with Linear Systems)
Cat and Mouse (Modeling with Linear Systems) - Metric
Solving Linear Systems (Slope-Intercept Form)

G.2.2: Measurements of Two-Dimensional Shapes and Figures

G.2.2.1: Use and/or compare measurements of angles.

G.2.2.1.1: Use properties of angles formed by intersecting lines to find the measures of missing angles.

Investigating Angle Theorems
Triangle Angle Sum

G.2.2.1.2: Use properties of angles formed when two parallel lines are cut by a transversal to find the measures of missing angles.

Constructing Parallel and Perpendicular Lines
Triangle Angle Sum

G.2.2.2: Use and/or develop procedures to determine or describe measures of perimeter, circumference, and/or area. (May require conversions within the same system.)

G.2.2.2.2: Find the measurement of a missing length, given the perimeter, circumference, or area.

Area of Parallelograms
Area of Triangles
Circumference and Area of Circles
Perimeter and Area of Rectangles

G.2.2.2.3: Find the side lengths of a polygon with a given perimeter to maximize the area of the polygon.

Perimeter and Area of Rectangles

G.2.2.3: Describe how a change in one dimension of a two-dimensional figure affects other measurements of that figure.

G.2.2.3.1: Describe how a change in the linear dimension of a figure affects its perimeter, circumference, and area (e.g., How does changing the length of the radius of a circle affect the circumference of the circle?).

Circumference and Area of Circles
Perimeter and Area of Rectangles

G.2.2.4: Apply probability to practical situations.

G.2.2.4.1: Use area models to find probabilities.

Geometric Probability

G.2.3: Measurements of Three-Dimensional Shapes and Figures

G.2.3.1: Use and/or develop procedures to determine or describe measures of surface area and/or volume. (May require conversions within the same system.)

G.2.3.1.1: Calculate the surface area of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheet.

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

G.2.3.1.2: Calculate the volume of prisms, cylinders, cones, pyramids, and/or spheres. Formulas are provided on a reference sheet.

Measuring Volume
Prisms and Cylinders
Pyramids and Cones

G.2.3.1.3: Find the measurement of a missing length given the surface area or volume.

Prisms and Cylinders
Pyramids and Cones

G.2.3.2: Describe how a change in one dimension of a three-dimensional figure affects other measurements of that figure.

G.2.3.2.1: Describe how a change in the linear dimension of a figure affects its surface area or volume (e.g., How does changing the length of the edge of a cube affect the volume of the cube?).

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