Geometry FlexBook® for Middle School

Geometry FlexBook® for High School

For Middle School

For High School

Levels are CK-12's student achievement levels.

Basic
Students matched to this level have a partial mastery of prerequisite knowledge and skills fundamental for proficient work.

At Grade (Proficient)
Students matched to this level have demonstrated competency over challenging subject matter, including subject matter knowledge, application of such knowledge to real-world situations, and analytical skills appropriate to subject matter.

Advanced
Students matched to this level are ready for material that requires superior performance and mastery.

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- Definitions and Introduction to Proof
- Basic Geometric Definitions
- Midpoints and Segment Bisectors
- Distance Between Two Points
- Ruler Postulate and Segment Addition Postulate
- Points that Partition Line Segments
- Angles
- Identification of Angles by Vertex and Ray
- Angle Classification
- Angles and Measurement
- Congruent Angles and Angle Bisectors
- Angle Measurement
- Angles at a Point
- Angle Bisectors
- Bisectors of Line Segments and Angles
- Angle Pairs
- Complementary Angles
- Supplementary Angles
- Linear Pairs
- Vertical Angles
- Supplementary and Complementary Angle Pairs
- Copies of Line Segments and Angles
- Polygon Classification
- Regular and Irregular Polygons
- Constructions of Regular Polygons
- Geometry Software for Constructions
- Classifying Polygons by Angles
- Classifying Polygons by Sides
- Polygon Classification in the Coordinate Plane
- Types of Reasoning
- Inductive Reasoning
- Inductive Reasoning from Patterns
- Visual Patterns
- Number Patterns
- Conjectures and Counterexamples
- Problem Solving Plan, Solve a Simpler Problem
- Deductive Reasoning
- Inductive versus Deductive Reasoning
- Truth Tables
- And and Or Statements
- If-Then Statements
- Converse, Inverse, and Contrapositive
- Negative Statements
- Indirect Proof in Algebra and Geometry
- Properties of Equality and Congruence
- Properties of Congruence
- Two-Column Proofs
- Proofs: Angle Pairs and Segments
- Applications of Line and Angle Theorems

- Parallel and Perpendicular Lines
- Lines and Angles
- Intersecting and Parallel Lines
- Parallel and Skew Lines
- Properties of Parallel Lines
- Corresponding Angles
- Alternate Interior Angles
- Alternate Exterior Angles
- Same Side Interior Angles
- Perpendicular Lines
- Perpendicular Transversals
- Parallel and Perpendicular Lines in the Coordinate Plane
- Slope in the Coordinate Plane
- Parallel Lines in the Coordinate Plane
- Perpendicular Lines in the Coordinate Plane
- Distance Formula in the Coordinate Plane
- Distance Between Parallel Lines
- Parallel and Perpendicular Line Constructions

- Triangle Relationships
- Triangle Sums
- Angle Measures in Given Triangles
- Triangle Sum Theorem
- Exterior Angles Theorems
- Congruent Figures
- Congruent Triangles
- Congruence Statements
- Third Angle Theorem
- Congruence Properties
- Corresponding Parts of Congruent Figures
- Triangle Congruence
- Comparing Angles and Sides in Triangles
- SSS Triangle Congruence
- SAS Triangle Congruence
- ASA and AAS Triangle Congruence
- HL Triangle Congruence
- Triangle Classification
- Triangle Classification by Angles
- Isosceles Triangles
- Equilateral Triangles
- Triangle Classification by Side Lengths
- Triangle Identification as Similar, Congruent, or Neither
- Midsegments of a Triangle
- Midsegment Theorem
- Bisectors in Triangles
- Perpendicular Bisectors
- Angle Bisectors in Triangles
- Medians
- Altitudes
- Triangle Inequality Theorem
- Theorems about Congruence in Triangles

- Quadrilateral Classification
- Angles in Polygons
- Relation of Polygon Sides to Angles and Diagonals
- Interior Angles in Convex Polygons
- Angle Measures in Given Quadrilaterals
- Exterior Angles in Convex Polygons
- Parallelograms
- Quadrilaterals that are Parallelograms
- Parallelograms in the Coordinate Plane
- Parallelogram Classification
- Trapezoids
- Kites
- Applications of Quadrilateral Theorems

- Similarity
- Ratios and Proportions
- Forms of Ratios
- Proportion Properties
- Similar Polygons and Scale Factors
- Scale Factor of Similar Polygons
- Corresponding Parts of Similar Figures
- Unknown Measures of Similar Figures
- Similarity by AA, SSS, SAS
- AA Similarity
- SSS Similarity
- SAS Similarity
- Indirect Measurement
- Proportionality Relationships
- Triangle Proportionality
- Parallel Lines and Transversals
- Proportions with Angle Bisectors
- Similarity Transformations
- Dilation
- Dilation in the Coordinate Plane
- Rules for Dilations
- Self-Similarity
- Circle Similarity

- Pythagorean Theorem and Pythagorean Triples
- Applications of the Pythagorean Theorem
- Proofs and Use of the Pythagorean Theorem
- Pythagorean Triples
- Distance Formula and the Pythagorean Theorem
- Converse of the Pythagorean Theorem
- Using Similar Right Triangles
- Inscribed Similar Triangles
- Special Right Triangles
- 45-45-90 Right Triangles
- 30-60-90 Right Triangles
- Trigonometric Ratios
- Sine, Cosine, Tangent
- Sine Identification
- Cosine Identification
- Tangent Identification
- Applications of Sine
- Applications of Cosine
- Applications of Tangent
- Sine and Cosine of Complementary Angles
- Trigonometric Ratios with a Calculator
- Trigonometry Word Problems
- Inverse Trigonometric Ratios
- Laws of Sines and Cosines
- Introduction to Law of Sines
- Introduction to Law of Cosines

- Parts of Circles
- Tangent Lines
- Arcs in Circles
- Central Angles and Arcs
- Chords in Circles
- Inscribed in Circles
- Inscribed Angles in Circles
- Inscribed Quadrilaterals in Circles
- Angles On and Inside a Circle
- Angles Outside a Circle
- Segments of Chords, Secants, and Tangents
- Segments from Chords
- Segments from Secants
- Segments from Secants and Tangents
- Circles in the Coordinate Plane
- Graphing a Circle in the Coordinate Plane
- Finding the Equation of a Circle
- Inscribed and Circumscribed Circles of Triangles
- Pi

- Perimeter, Circumference, Area, Surface Area, Volume
- Area and Perimeter of Triangles
- Comparing Rectangles, Squares, Parallelograms
- Perimeter of Parallelograms
- Area and Perimeter of Rectangles
- Perimeter of Squares and Rectangles
- Area of Squares and Rectangles
- Unknown Dimensions Using Formulas
- Comparing Trapezoids, Rhombi, and Kites
- Area and Perimeter of Trapezoids
- Area and Perimeter of Rhombuses and Kites
- Similar Polygons
- Area and Perimeter of Similar Polygons
- Circumference
- Circle Circumference
- Diameter or Radius of a Circle Given Circumference
- Arc Length
- Triangle Area
- Unknown Dimensions of Triangles
- Area of Rectangles, Squares, Parallelograms
- Area of a Parallelogram
- Area of Rectangles
- Area of Squares
- Unknown Dimensions of Parallelograms
- Estimation of Parallelogram Area in Scale Drawings
- Area of Regular Polygons
- Area of Composite Shapes
- Areas of Combined Figures Involving Circles
- Area of Composite Shapes Involving Triangles
- Area of a Circle
- Radius or Diameter of a Circle Given Area
- Area of Sectors and Segments
- Surface Area and Volume of Solids
- Surface Area and Volume of Prisms
- Surface Area of Prisms
- Surface Area of Rectangular Prisms
- Surface Area of Triangular Prisms
- Surface Area and Volume of Cylinders
- Surface Area of Cylinders
- Heights of Cylinders Given Surface Area
- Surface Area and Volume of Pyramids
- Surface Area and Volume of Cones
- Volume
- Volume of Prisms
- Volume of Prisms Using Unit Cubes
- Volume of Rectangular Prisms
- Volume of Triangular Prisms
- Volume of Cylinders
- Heights of Cylinders Given Volume
- Volume of Pyramids
- Volume of Cones
- Spheres
- Surface Area of Spheres
- Volume of Sphere
- Composite Solids
- Classification of Solid Figures
- Polyhedrons
- Euler's Theorem
- Faces, Edges, and Vertices of Solids
- Solids Created by Rotations
- Cross-Sections and Nets
- Modeling in Three Dimensions
- Density Problems
- Design Problems in Three Dimensions
- Area and Volume of Similar Solids
- Similar Solids

- Rigid Transformations
- Lines of Symmetry
- Reflection Symmetry
- Rotation Symmetry
- Translations and Vectors
- Geometric Translations
- Graphs of Translations
- Rules for Translations
- Integer Translations, Paths Between Points
- Geometry Software for Translations
- Reflections
- Graphs of Reflections
- Rules for Reflections
- Geometry Software for Reflections
- Rotations
- Defining Rotations
- Graphs of Rotations
- Geometry Software for Rotations
- Composition of Transformations
- Order of Composite Transformations
- Notation for Composite Transformations
- Tessellations
- Transformation Classification
- Translations, Rotations, and Reflections

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