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Concepts
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Basics of Geometry
Geometry Terms
Shapes
2D Shapes
Identify Shapes
Identify Less Common Shapes
Composite Shapes
Identify Area Through Decomposition
Identify Area Through Composition
Line Segments
Definition of Line Segment
Midpoints and Segment Bisectors
Midpoint Formula
Points that Partition Line Segments
Angles
Introduction to Angles
Identification of Angles by Vertex and Ray
Measuring Angles
Classifying Angles
Congruent Angles and Angle Bisectors
Angles in the Sexigesimal System
Operations with Angles in the Sexigesimal System
Constructions and Bisectors
Construct Copies of Line Segments and Angles
Geometry Software for Construction
Angle Pairs
Angle Properties and Theorems
Complementary Angles
Supplementary Angles
Missing Measures of Complementary and Supplementary Angles
Vertical Angles
Parallel Lines and Angles
Applications of Missing Angles
Basic Polygons
Classify Polygons
Vertices and Sides
Polygon Classification in the Coordinate Plane
Reasoning and Proof
Patterns and Reasoning
Basic Visual Patterns
Identify Basic Pattern Type
Number Patterns
Reasoning Types
Inductive Reasoning from Patterns
Conjectures and Counterexamples
Deductive Reasoning
Magic Squares
Logic Statements
Truth Tables
And and Or Statements
Negative Statements
If Then Statements
Converse, Inverse, and Contrapositive Statements
Properties and Proofs
Introduction to Proofs
Properties of Equality and Congruence
Proofs: Angle Pairs and Segments
Proofs involving Parallel and Perpendicular Lines
Parallelogram Proofs
Applications and Proofs Involving Line and Angle Theorems
Proofs Involving Triangles
Indirect Proof in Algebra and Geometry
Lines
Line Types
Parallel and Skew Lines
Transversals
Parallel Lines and Transversals
Corresponding Angles
Alternate Interior Angles
Alternate Exterior Angles
Same Side Interior Angles
Angles and Perpendicular Lines
Lines in the Coordinate Plane
Parallel Lines in the Coordinate Plane
Perpendicular Lines in the Coordinate Plane
Coordinate Plane Proofs
Line Construction
Construct Parallel and Perpendicular Lines
Triangles
Classifying Triangles
Classify Triangles
Classify Triangles by Angle Measurement
Classify Triangles by Side Measurement
Isosceles Triangles
Equilateral Triangles
Triangle Area and Perimeter
Area and Perimeter of Triangles
Triangle Area
Unknown Dimensions of Triangles
Triangle Congruency
CPCTC
Congruence Statements
Third Angle Theorem
Congruent Triangles
SSS
SAS
ASA and AAS
HL
Triangle Relationships
Triangle Angle Sum Theorem
Exterior Angles and Theorems
Midsegment Theorem
Perpendicular Bisectors
Angle Bisectors in Triangles
Concurrence and Constructions
Medians
Altitudes
Comparing Angles and Sides in Triangles
Triangle Inequality Theorem
Angle Relationships in Triangles
Applications and Proofs Involving Triangle Theorems
Right Triangles
Pythagorean Theorem
The Pythagorean Theorem
Basics of Pythagorean Theorem
Pythagorean Theorem to Classify Triangles
Pythagorean Triples
Proofs of the Pythagorean Theorem
Converse of the Pythagorean Theorem
Pythagorean Theorem Applications
Right Triangles in Algebra
Pythagorean Theorem and its Converse
Solving Equations Using the Pythagorean Theorem
Applications Using the Pythagorean Theorem
Distance Formula
Distance and Triangle Classification Using the Pythagorean Theorem
Distance Formula and the Pythagorean Theorem
Distance Between Parallel Lines
The Distance Formula and Algebra
Applications of the Distance Formula
Special Triangles
Special Right Triangles and Ratios
45-45-90 Right Triangles
30-60-90 Right Triangles
Quadrilaterals and Polygons
Basic Squares and Rectangles
Squares
Rectangles
Square and Rectangle Area and Perimeter
Perimeter of Squares and Rectangles
Area of Squares and Rectangles
Unknown Dimensions of Squares and Rectangles
Quadrilaterals
Quadrilateral Classification
Parallelogram Classification
Parallelograms
Area of a Parallelogram
Unknown Dimensions of Parallelograms
Estimation of Parallelogram Area in Scale Drawings
Trapezoids
Area and Perimeter of Trapezoids
Area of Parallelograms: Squares, Rectangles and Trapezoids
Kites
Area and Perimeter of Rhombuses and Kites
Area and Perimeter of Composite Shapes
Quadrilateral Classification in the Coordinate Plane
Area and Perimeter of Shapes on a Coordinate Plane
Applications and Proofs Involving Quadrilateral Theorems
Polygons
Area and Perimeter of Triangles and Quadrilaterals
Regular and Irregular Polygons
Area of Regular and Irregular Polygons
Perimeter of a Polygon
Area and Perimeter of Similar Polygons
Construct Regular Polygons
Definition of Congruence
Congruent Polygons
Corresponding Parts of Congruent Figures
Polygon Angle Measures
Overview of Polygon Angle Measures
Determine Missing Angle Measures
Interior Angles in Convex Polygons
Exterior Angles in Convex Polygons
Circles
Parts of a Circle
Semicircles and Quarter Circles
Identify Circle Components
Use Diameter, Radius and Pi
Circumference
Diameter or Radius of a Circle Given Circumference
Area of a Circle
Circle Area
Areas of Combined Figures Involving Semicircles
Radius or Diameter of a Circle Given Area
Arcs and Chords
Arcs in Circles
Understand Arcs and Sectors
Area of Sectors and Segments
Central Angles
Arc Length
Chords and Central Angle Arcs
Segments from Chords
Circles and Angles
Inscribed Angles in Circles
Inscribed Quadrilaterals in Circles
Angles On and Inside a Circle
Angles Outside a Circle
Tangent Lines and Theorems
Tangent Lines
Area and Circumference of a Circle
Applications of Area and Circumference
Area and Perimeter of Inscribed Polygons
Secants
Intersecting Secants Theorem
Tangent Secant Theorem
Circles in the Coordinate Plane
Inscribed and Circumscribed Circles of Triangles
Similarity
Similar Figures
Definition of Similarity
Ratio and Proportion in Similar Figures
Similar Polygons and Scale Factors
Corresponding Parts of Similar Figures
Indirect Measurement
Indirect Measurement Applications
Triangle Similarity
AA Similarity
SSS Similarity
SAS Similarity
Triangle Proportionality
Proportional Triangles
Inscribed Similar Triangles
Parallel Lines, Transversals, and Proportionality
Proportions and Angle Bisectors
Theorems Involving Similarity
Dilation
Dilation of a Shape
Properties of Dilations
Dilation in the Coordinate Plane
Mapping Dilations
Self-Similarity and Fractals
Rigid Transformations
Identify Transformation Types
Symmetry
Lines of Symmetry
Reflection Symmetry
Rotation Symmetry
3D Rotational Symmetry
Axial Symmetry
Central Symmetry
Translations
Geometric Translation
Properties of Translations
Sliding Figures
Translation Notation
Translations in the Coordinate Plane
Geometry Software for Translations
Translation Applications in Circle Similarity
Rotations
Defining Rotation
Properties of Rotations
Rotation Rules
Geometry Software and Graphing Rotations
Rotations in the Coordinate Plane
Reflections
Defining Reflection
Properties of Reflections
Rules for Reflections
Reflections in the Coordinate Plane
Geometry Software for Reflections
Reflecting Figures
Composition of Transformations
Composite Transformations
Notation for Composite Transformations
Sequences of Translations and Reflections
Sequences of Rotations
Tessellations
Solid Figures
Polyhedrons
Faces, Edges, and Vertices of Solids
Cross-Sections and Nets
Nets
Cross Sections of Prisms
Cross Sections of Pyramids
Surface Area
Volume
Volume of Pyramids and Cones
Cross Sections and Basic Solids of Revolution
Surface Area of Prisms and Pyramids
Composite Solids
Surface Area of Composite Solids
Volume of Composite Solids
Area and Volume of Similar Solids
Surface Area and Volume Applications
Density Application Problems
Surface Area and Volume Optimization
Comparing Volumes
Prisms
Surface Area and Volume of Prisms
Surface Area of Prisms
Surface Area of Cubes and Rectangular Prisms
Surface Area of Triangular Prisms
Volume of Prisms
Volume of Prisms Using Unit Cubes
Volume of Rectangular Prisms
Volume of Triangular Prisms
Pyramids
Surface Area and Volume of Pyramids
Volume of Pyramids
Surface Area of Pyramids
Cylinders
Surface Area and Volume of Cylinders
Surface Area of Cylinders
Volume of Cylinders
Heights of Cylinders Given Surface Area or Volume
Dimensions of Cylinders Given the Volume
Cones
Surface Area and Volume of Cones
Surface Area of Cones
Volume of Cones
Dimensions of Cones Given Volume
Spheres
Surface Area and Volume of Spheres
Surface Area of Spheres
Volume of Spheres
Dimensions of Spheres Given Volume
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