Nguồn ngoài
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.
- Tác giả
- CK-12 Foundation
- Nhà xuất bản
- LibreTexts
- Nguồn
- LibreTexts
- Giấy phép
- CK-12
- Ngôn ngữ
- EN
- Danh mục
- Khoa học cơ bản
Mục lục· 214 mục
- 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