CO: Congruence

CO.A: Experiment with transformations in the plane.

CO.A.1: Define angle, circle, perpendicular line, parallel line, line segment and ray based on the undefined notions of point, line, distance along a line and distance around a circular arc.

Circles
Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Inscribed Angles
Parallel, Intersecting, and Skew Lines

CO.A.2: Represent transformations in the plane, and describe them as functions that take points in the plane as inputs and give other points as outputs.

Dilations
Reflections
Rotations, Reflections, and Translations
Translations

CO.A.3: Describe the rotational symmetry and lines of symmetry of two-dimensional figures.

Holiday Snowflake Designer

CO.A.4: Develop definitions of rotations, reflections and translations in terms of angles, circles, perpendicular lines, parallel lines and line segments.

Circles
Dilations
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations

CO.A.5: Demonstrate the ability to rotate, reflect or translate a figure, and determine a possible sequence of transformations between two congruent figures.

Dilations
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations

CO.B: Understand congruence in terms of rigid motions.

CO.B.1: Develop the definition of congruence in terms of rigid motions.

Absolute Value with Linear Functions
Circles
Dilations
Holiday Snowflake Designer
Proving Triangles Congruent
Reflections
Rotations, Reflections, and Translations
Similar Figures
Translations

CO.B.2: Develop the criteria for triangle congruence from the definition of congruence in terms of rigid motions.

Congruence in Right Triangles
Constructing Congruent Segments and Angles
Proving Triangles Congruent

CO.C: Prove geometric theorems.

CO.C.1: Prove theorems about lines and angles.

Investigating Angle Theorems

CO.C.2: Prove theorems about triangles.

Pythagorean Theorem
Triangle Angle Sum
Triangle Inequalities

CO.C.3: Prove theorems about polygons.

Parallelogram Conditions
Special Parallelograms

CO.D: Make geometric constructions.

CO.D.1: Construct geometric figures using various tools and methods.

Constructing Congruent Segments and Angles
Constructing Parallel and Perpendicular Lines
Segment and Angle Bisectors

SRT: Similarity, Right Triangles, and Trigonometry

SRT.A: Understand similarity in terms of similarity transformations.

SRT.A.1: Construct and analyze scale changes of geometric figures.

Dilations
Similar Figures

SRT.A.2: Use the definition of similarity to decide if figures are similar and to solve problems involving similar figures.

Circles
Dilations
Perimeters and Areas of Similar Figures
Similar Figures
Similarity in Right Triangles

SRT.B: Prove theorems involving similarity.

SRT.B.1: Use congruence and similarity criteria for triangles to solve problems and to prove relationships in geometric figures.

Dilations
Perimeters and Areas of Similar Figures
Similarity in Right Triangles

SRT.C: Define trigonometric ratios, and solve problems involving right triangles.

Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

SRT.C.1: Understand that side ratios in right triangles define the trigonometric ratios for acute angles.

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

SRT.C.3: Use trigonometric ratios and the Pythagorean Theorem to solve right triangles.

Cosine Function
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard
Sine Function
Sine, Cosine, and Tangent Ratios
Tangent Function

C: Circles

C.A: Understand and apply theorems about circles.

C.A.2: Identify and describe relationships among inscribed angles, radii and chords of circles.

Chords and Arcs
Circumference and Area of Circles
Inscribed Angles

C.B: Find arc lengths and areas of sectors of circles.

C.B.1: Derive the formula for the length of an arc of a circle.

Chords and Arcs

C.B.2: Derive the formula for the area of a sector of a circle.

Chords and Arcs

GPE: Exploring Geometric Properties with Equations

GPE.A: Translate between the geometric description and the equation for a conic section.

GPE.A.1: Derive the equation of a circle.

Circles
Distance Formula
Pythagorean Theorem
Pythagorean Theorem with a Geoboard

GPE.A.2: Derive the equation of a parabola given a focus and directrix.

Parabolas

GPE.B: Use coordinates to prove geometric theorems algebraically.

GPE.B.4: Use coordinates to compute perimeters of polygons and areas of triangles and rectangles.

Distance Formula

GMD: Geometric Measurement and Dimension

GMD.A: Explain volume formulas and use them to solve problems.

GMD.A.1: Give an informal argument for the formulas for the circumference of a circle, area of a circle, volume of a cylinder, pyramid and cone.

Circumference and Area of Circles
Prisms and Cylinders
Pyramids and Cones

GMD.A.2: Use volume formulas for cylinders, pyramids, cones, spheres and composite figures to solve problems.

Prisms and Cylinders
Pyramids and Cones

CP: Conditional Probability and Rules of Probability

CP.A: Understand independence and conditional probability and use them to interpret data.

CP.A.1: Describe events as subsets of a sample space using characteristics of the outcomes, or as unions, intersections or complements of other events.

Independent and Dependent Events
Probability Simulations
Theoretical and Experimental Probability

CP.A.2: Understand the definition of independent events and use it to solve problems.

Independent and Dependent Events
Theoretical and Experimental Probability

CP.A.3: Calculate conditional probabilities of events.

Independent and Dependent Events

CP.A.5: Recognize and explain the concepts of conditional probability and independence in a context.

Independent and Dependent Events

CP.A.6: Apply and interpret the Addition Rule for calculating probabilities.

Binomial Probabilities

CP.A.7: Apply and interpret the general Multiplication Rule in a uniform probability model.

Independent and Dependent Events

CP.A.8: Use permutations and combinations to solve problems.

Binomial Probabilities
Permutations and Combinations