sleep

- 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 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
- 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
- Midsegment Theorem
- Perpendicular Bisectors
- Angle Bisectors in Triangles
- Medians
- Altitudes
- Triangle Inequality Theorem
- Theorems about Congruence in Triangles

- Quadrilateral Classification
- 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 Angles in Circles
- Inscribed Quadrilaterals in Circles
- Angles On and Inside a Circle
- Angles Outside a Circle
- 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
- Area and Perimeter of Trapezoids
- Area and Perimeter of Rhombuses and Kites
- 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
- 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

Back to the top of the page ↑

+

Contribute a better translation