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Geometry
Geometry is one of the oldest branches of mathematics and is concerned with properties of space that are related with distance, shape, size, and relative position of figures.
- Author
- CK-12 Foundation
- Publisher
- LibreTexts
- Source
- LibreTexts
- License
- CK-12
- Language
- EN
- Category
- Basic Sciences
Contents· 214 sections
- 01: Basics of Geometry
- 1.01: Geometry Terms
- 1.02: Shapes
- 1.03: Definition of Line segments
- 1.04: Midpoints and Segment Bisector
- 1.05: Midpoint Formula
- 1.06: Points that Partition Line Segments
- 1.07: Introduction to Angles
- 1.08: Identification of Angles by Vertex and Ray
- 1.09: Measuring Angles
- 1.10: Classifying Angles
- 1.11: Congruent Angles and Angle Bisectors
- 1.12: Constructions and Bisectors
- 1.13: Angle Properties and Theorems
- 1.14: Complementary Angles
- 1.15: Supplementary Angles
- 1.16: Missing Measures of Complementary and Supplementary Angles
- 1.17: Vertical Angles
- 1.18: Classify Polygons
- 1.19: Vertices and Sides
- 1.20: Polygon Classification in the Coordinate Plane
- 02: Reasoning and Proof
- 2.01: Basic Visual Patterns
- 2.02: Identify Basic Pattern Type
- 2.03: Number Patterns
- 2.04: Reasoning Types
- 2.05: Inductive Reasoning from Patterns
- 2.06: Conjectures and Counterexamples
- 2.07: Deductive Reasoning
- 2.08: Truth Tables
- 2.09: And and Or Statements
- 2.10: Negative Statements
- 2.11: If Then Statements
- 2.12: Converse Inverse and Contrapositive Statements
- 2.13: Introduction to Proofs
- 2.14: Properties of Equality and Congruence
- 2.15: Proofs- Angle Pairs and Segments
- 2.16: Parallelogram Proofs
- 2.17: Proofs Involving Triangles
- 2.18: Indirect Proof in Algebra and Geometry
- 03: Lines
- 3.01: Line Types
- 3.02: Parallel and Skew Lines
- 3.03: Parallel Lines and Transversals
- 3.04: Corresponding Angles
- 3.05: Alternate Interior Angles
- 3.06: Alternate Exterior Angles
- 3.07: Same Side Interior Angles
- 3.08: Angles and Perpendicular Lines
- 3.09: Parallel Lines in the Coordinate Plane
- 3.10: Perpendicular Lines in the Coordinate Plane
- 3.11: Line Construction
- 04: Triangles
- 4.01: Classify Triangles
- 4.02: Classify Triangles by Angle Measurement
- 4.03: Classify Triangles by Side Measurement
- 4.04: Isosceles Triangles
- 4.05: Equilateral Triangles
- 4.06: Area and Perimeter of Triangles
- 4.07: Triangle Area
- 4.08: Unknown Dimensions of Triangles
- 4.09: CPCTC
- 4.10: Congruence Statements
- 4.11: Third Angle Theorem
- 4.12: Congruent Triangles
- 4.13: SSS
- 4.14: SAS
- 4.15: ASA and AAS
- 4.16: HL
- 4.17: Triangle Angle Sum Theorem
- 4.18: Exterior Angles and Theorems
- 4.19: Midsegment Theorem
- 4.20: Perpendicular Bisectors
- 4.21: Angle Bisectors in Triangles
- 4.22: Concurrence and Constructions
- 4.23: Medians
- 4.24: Altitudes
- 4.25: Comparing Angles and Sides in Triangles
- 4.26: Triangle Inequality Theorem
- 4.27: The Pythagorean Theorem
- 4.28: Basics of Pythagorean Theorem
- 4.29: Pythagorean Theorem to Classify Triangles
- 4.30: Pythagorean Triples
- 4.31: Converse of the Pythagorean Theorem
- 4.32: Pythagorean Theorem Applications
- 4.33: Pythagorean Theorem and its Converse
- 4.34: Solving Equations Using the Pythagorean Theorem
- 4.35: Applications Using the Pythagorean Theorem
- 4.36: Distance and Triangle Classification Using the Pythagorean Theorem
- 4.37: Distance Formula and the Pythagorean Theorem
- 4.38: Distance Between Parallel Lines
- 4.39: The Distance Formula and Algebra
- 4.40: Applications of the Distance Formula
- 4.41: Special Right Triangles and Ratios
- 4.42: 45-45-90 Right Triangles
- 4.43: 30-60-90 Right Triangles
- 05: Quadrilaterals and Polygons
- 5.01: Squares
- 5.02: Rectangles
- 5.03: Square and Rectangle Area and Perimeter
- 5.04: Perimeter of Squares and Rectangles
- 5.05: Area of Squares and Rectangles
- 5.06: Unknown Dimensions of Squares and Rectangles
- 5.07: Quadrilateral Classification
- 5.08: Parallelogram Classification
- 5.09: Parallelograms
- 5.10: Area of a Parallelogram
- 5.11: Unknown Dimensions of Parallelograms
- 5.12: Estimation of Parallelogram Area in Scale Drawings
- 5.13: Trapezoids
- 5.14: Area and Perimeter of Trapezoids
- 5.15: Area of Parallelograms- Squares Rectangles and Trapezoids
- 5.16: Kites
- 5.17: Area and Perimeter of Rhombuses and Kites
- 5.18: Area and Perimeter of Composite Shapes
- 5.19: Quadrilateral Classification in the Coordinate Plane
- 5.20: Regular and Irregular Polygons
- 5.21: Area of Regular and Irregular Polygons
- 5.22: Area and Perimeter of Similar Polygons
- 5.23: Construct Regular Polygons
- 5.24: Congruent Polygons
- 5.25: Corresponding Parts of Congruent Figures
- 5.26: Determine Missing Angle Measures
- 5.27: Interior Angles in Convex Polygons
- 5.28: Exterior Angles in Convex Polygons
- 06: Circles
- 6.01: Semicircles and Quarter Circles
- 6.02: Identify Circle Components
- 6.03: Use Diameter Radius and Pi
- 6.04: Circumference
- 6.05: Diameter or Radius of a Circle Given Circumference
- 6.06: Circle Area
- 6.07: Areas of Combined Figures Involving Semicircles
- 6.08: Radius or Diameter of a Circle Given Area
- 6.09: Arcs in Circles
- 6.10: Area of Sectors and Segments
- 6.11: Arc Length
- 6.12: Chords and Central Angle Arcs
- 6.13: Segments from Chords
- 6.14: Inscribed Angles in Circles
- 6.15: Inscribed Quadrilaterals in Circles
- 6.16: Angles On and Inside a Circle
- 6.17: Angles Outside a Circle
- 6.18: Tangent Lines
- 6.19: Intersecting Secants Theorem
- 6.20: Tangent Secant Theorem
- 6.21: Circles in the Coordinate Plane
- 07: Similarity
- 7.01: Similar Figures
- 7.02: Ratio and Proportion in Similar Figures
- 7.03: Similar Polygons and Scale Factors
- 7.04: Corresponding Parts of Similar Figures
- 7.05: Indirect Measurement
- 7.06: Indirect Measurement Applications
- 7.07: AA Similarity
- 7.08: SSS Similarity
- 7.09: SAS Similarity
- 7.10: Proportional Triangles
- 7.11: Inscribed Similar Triangles
- 7.12: Parallel Lines Transversals and Proportionality
- 7.13: Proportions and Angle Bisectors
- 7.14: Theorems Involving Similarity
- 7.15: Dilation of a Shape
- 7.16: Dilation in the Coordinate Plane
- 7.17: Mapping Dilations
- 7.18: Self-Similarity and Fractals
- 08: Rigid Transformations
- 8.01: Identify Transformation Types
- 8.02: Lines of Symmetry
- 8.03: Reflection Symmetry
- 8.04: Rotation Symmetry
- 8.05: Geometric Translation
- 8.06: Sliding Figures
- 8.07: Geometry Software for Translations
- 8.08: Translation Applications in Circle Similarity
- 8.09: Translation Notation
- 8.10: Defining Rotation
- 8.11: Rotation Rules
- 8.12: Geometry Software and Graphing Rotations
- 8.13: Defining Reflection
- 8.14: Rules for Reflections
- 8.15: Geometry Software for Reflections
- 8.16: Reflecting Figures
- 8.17: Composite Transformations
- 8.18: Notation for Composite Transformations
- 8.19: Tessellations
- 09: Solid Figures
- 9.01: Polyhedrons
- 9.02: Faces Edges and Vertices of Solids
- 9.03: Cross-Sections and Nets
- 9.04: Surface Area
- 9.05: Volume
- 9.06: Cross Sections and Basic Solids of Revolution
- 9.07: Composite Solids
- 9.08: Area and Volume of Similar Solids
- 9.09: Surface Area and Volume Applications
- 9.10: Surface Area and Volume of Prisms
- 9.11: Surface Area of Prisms
- 9.12: Volume of Prisms
- 9.13: Volume of Prisms Using Unit Cubes
- 9.14: Volume of Rectangular Prisms
- 9.15: Volume of Triangular Prisms
- 9.16: Surface Area and Volume of Pyramids
- 9.17: Volume of Pyramids
- 9.18: Surface Area and Volume of Cylinders
- 9.19: Surface Area of Cylinders
- 9.20: Volume of Cylinders
- 9.21: Heights of Cylinders Given Surface Area or Volume
- 9.22: Surface Area and Volume of Cones
- 9.23: Surface Area of Cones
- 9.24: Volume of Cones
- 9.25: Surface Area and Volume of Spheres
- 9.26: Surface Area of Spheres
- 9.27: Volume of Spheres