Advanced Geometry Explorations

          Module 1: Foundations of Geometry

Section 1: Basic Elements of Geometry
Lesson 1: Understanding Points
Module 1, Section 1, Lesson 1: Understanding Points
Lesson 2: Understanding Lines
Module 1, Section 1, Lesson 2: Understanding Lines

Section 2: Exploring Planes and Space
Lesson 1: Defining Planes
Module 1, Section 2, Lesson 1: Defining Planes
Lesson 2: Relationships in Space
Module 1, Section 2, Lesson 2: Relationships in Space

Section 3: Segments, Rays, and Angles
Lesson 1: Line Segments and Rays Explained
Module 1, Section 3, Lesson 1: Line Segments and Rays Explained
Lesson 2: Introduction to Angles
Module 1, Section 3, Lesson 2: Introduction to Angles

Section 4: Measuring Lengths and Angles
Lesson 1: Techniques for Measuring Distances
Module 1, Section 4, Lesson 1: Techniques for Measuring Distances
Lesson 2: Tools for Angle Measurement
Module 1, Section 4, Lesson 2: Tools for Angle Measurement

Section 5: Postulates and Axioms in Geometry
Lesson 1: The Role of Postulates in Geometry
Module 1, Section 5, Lesson 1: The Role of Postulates in Geometry
Lesson 2: Fundamental Axioms
Module 1, Section 5, Lesson 2: Fundamental Axioms


Module 2: Geometric Constructions and Tools

Section 1: Introduction to Geometric Tools
Lesson 1: Using a Compass
Module 2, Section 1, Lesson 1: Using a Compass
Lesson 2: Using a Straightedge
Module 2, Section 1, Lesson 2: Using a Straightedge

Section 2: Basic Construction Techniques
Lesson 1: Constructing Perpendicular Lines
Module 2, Section 2, Lesson 1: Constructing Perpendicular Lines
Lesson 2: Bisecting Angles
Module 2, Section 2, Lesson 2: Bisecting Angles

Section 3: Drawing and Interpreting Diagrams
Lesson 1: Reading Geometric Diagrams
Module 2, Section 3, Lesson 1: Reading Geometric Diagrams
Lesson 2: Sketching Basic Figures
Module 2, Section 3, Lesson 2: Sketching Basic Figures

Section 4: Precision in Constructions
Lesson 1: Accuracy and Scale in Drawings
Module 2, Section 4, Lesson 1: Accuracy and Scale in Drawings
Lesson 2: Refining Construction Techniques
Module 2, Section 4, Lesson 2: Refining Construction Techniques

Section 5: Putting Constructions to Use
Lesson 1: Constructing Triangles and Polygons
Module 2, Section 5, Lesson 1: Constructing Triangles and Polygons
Lesson 2: Real-World Construction Applications
Module 2, Section 5, Lesson 2: Real-World Construction Applications


Module 3: Measurements and Calculations in Geometry

Section 1: Understanding Length and Perimeter
Lesson 1: Concepts of Length and Distance
Module 3, Section 1, Lesson 1: Concepts of Length and Distance
Lesson 2: Calculating Perimeters
Module 3, Section 1, Lesson 2: Calculating Perimeters

Section 2: Areas of Basic Figures
Lesson 1: Area of Triangles and Rectangles
Module 3, Section 2, Lesson 1: Area of Triangles and Rectangles
Lesson 2: Area of Circles and Other Shapes
Module 3, Section 2, Lesson 2: Area of Circles and Other Shapes

Section 3: Introduction to Volume and Capacity
Lesson 1: Understanding Three-Dimensional Measurement
Module 3, Section 3, Lesson 1: Understanding Three-Dimensional Measurement
Lesson 2: Volume of Simple Solids
Module 3, Section 3, Lesson 2: Volume of Simple Solids

Section 4: Angle Measurement and Calculation
Lesson 1: Degrees, Radians, and Their Uses
Module 3, Section 4, Lesson 1: Degrees, Radians, and Their Uses
Lesson 2: Calculating Angles in Figures
Module 3, Section 4, Lesson 2: Calculating Angles in Figures

Section 5: Scale and Proportionality in Geometry
Lesson 1: The Concept of Scale in Diagrams
Module 3, Section 5, Lesson 1: The Concept of Scale in Diagrams
Lesson 2: Proportional Relationships in Figures
Module 3, Section 5, Lesson 2: Proportional Relationships in Figures


Module 4: Introduction to Proof and Logical Reasoning

Section 1: Fundamentals of Mathematical Reasoning
Lesson 1: What is a Mathematical Proof?
Module 4, Section 1, Lesson 1: What is a Mathematical Proof?
Lesson 2: Understanding Logical Arguments
Module 4, Section 1, Lesson 2: Understanding Logical Arguments

Section 2: Basic Proof Structures
Lesson 1: Direct Proof Methods
Module 4, Section 2, Lesson 1: Direct Proof Methods
Lesson 2: Proof by Contradiction Explained
Module 4, Section 2, Lesson 2: Proof by Contradiction Explained

Section 3: Building Arguments from Definitions
Lesson 1: Using Definitions in Proofs
Module 4, Section 3, Lesson 1: Using Definitions in Proofs
Lesson 2: Constructing Logical Statements
Module 4, Section 3, Lesson 2: Constructing Logical Statements

Section 4: Working with Postulates and Axioms in Proof
Lesson 1: Applying Postulates to Form Proofs
Module 4, Section 4, Lesson 1: Applying Postulates to Form Proofs
Lesson 2: Axioms as the Foundation for Reasoning
Module 4, Section 4, Lesson 2: Axioms as the Foundation for Reasoning

Section 5: Practice with Fundamental Proofs
Lesson 1: Proving Properties of Triangles
Module 4, Section 5, Lesson 1: Proving Properties of Triangles
Lesson 2: Exploring Quadrilateral Proofs
Module 4, Section 5, Lesson 2: Exploring Quadrilateral Proofs


Module 5: Connecting Theory to Real-World Applications

Section 1: Geometry in Nature and Art
Lesson 1: Patterns and Symmetry in Nature
Module 5, Section 1, Lesson 1: Patterns and Symmetry in Nature
Lesson 2: Geometry in Artistic Designs
Module 5, Section 1, Lesson 2: Geometry in Artistic Designs

Section 2: Geometry and Architecture
Lesson 1: Structural Shapes and Their Purposes
Module 5, Section 2, Lesson 1: Structural Shapes and Their Purposes
Lesson 2: The Role of Geometry in Building Design
Module 5, Section 2, Lesson 2: The Role of Geometry in Building Design

Section 3: Mapping and Navigation
Lesson 1: Basics of Map Reading and Scale
Module 5, Section 3, Lesson 1: Basics of Map Reading and Scale
Lesson 2: Geometric Concepts in Navigation
Module 5, Section 3, Lesson 2: Geometric Concepts in Navigation

Section 4: Technology and Geometric Design
Lesson 1: Computer-Aided Design (CAD) Fundamentals
Module 5, Section 4, Lesson 1: Computer-Aided Design (CAD) Fundamentals
Lesson 2: Geometry in Digital Modeling
Module 5, Section 4, Lesson 2: Geometry in Digital Modeling

Section 5: Project-Based Exploration of Geometry
Lesson 1: Hands-On Geometric Project Planning
Module 5, Section 5, Lesson 1: Hands-On Geometric Project Planning
Lesson 2: Presenting Geometric Solutions
Module 5, Section 5, Lesson 2: Presenting Geometric Solutions