Advanced Euclidean Geometry

          Module 1: Foundations of Euclidean Geometry

Section 1: Basic Terminology
- Lesson 1: What is a Point and a Line?
  Module 1, Section 1, Lesson 1: What is a Point and a Line?
- Lesson 2: Understanding Planes in Euclidean Space
  Module 1, Section 1, Lesson 2: Understanding Planes in Euclidean Space

Section 2: The Language of Geometry
- Lesson 1: Definitions – Line, Ray, and Segment
  Module 1, Section 2, Lesson 1: Definitions – Line, Ray, and Segment
- Lesson 2: Geometric Notation and Diagram Reading
  Module 1, Section 2, Lesson 2: Geometric Notation and Diagram Reading

Section 3: Tools and Constructions
- Lesson 1: Using a Ruler and Compass Effectively
  Module 1, Section 3, Lesson 1: Using a Ruler and Compass Effectively
- Lesson 2: Basic Geometric Constructions
  Module 1, Section 3, Lesson 2: Basic Geometric Constructions

Section 4: Axioms, Postulates, and Definitions
- Lesson 1: Euclid’s Postulates Explained
  Module 1, Section 4, Lesson 1: Euclid’s Postulates Explained
- Lesson 2: How Definitions Form the Basis of Geometry
  Module 1, Section 4, Lesson 2: How Definitions Form the Basis of Geometry

Section 5: Introduction to Proofs
- Lesson 1: What is a Geometric Proof?
  Module 1, Section 5, Lesson 1: What is a Geometric Proof?
- Lesson 2: Constructing a Simple Two-Column Proof
  Module 1, Section 5, Lesson 2: Constructing a Simple Two-Column Proof


Module 2: Similarity and Congruence Fundamentals

Section 1: Congruence Basics
- Lesson 1: Understanding Congruence in Figures
  Module 2, Section 1, Lesson 1: Understanding Congruence in Figures
- Lesson 2: Introduction to SSS and SAS Criteria
  Module 2, Section 1, Lesson 2: Introduction to SSS and SAS Criteria

Section 2: Similarity Basics
- Lesson 1: What Does Similarity Mean?
  Module 2, Section 2, Lesson 1: What Does Similarity Mean?
- Lesson 2: Scale Factors and Proportionality
  Module 2, Section 2, Lesson 2: Scale Factors and Proportionality

Section 3: Triangles – Congruence and Similarity
- Lesson 1: Criteria for Triangle Congruence
  Module 2, Section 3, Lesson 1: Criteria for Triangle Congruence
- Lesson 2: Recognizing Similar Triangles Using AA
  Module 2, Section 3, Lesson 2: Recognizing Similar Triangles Using AA

Section 4: Applications of Congruence
- Lesson 1: Side-Side-Side (SSS) in Problem Solving
  Module 2, Section 4, Lesson 1: Side-Side-Side (SSS) in Problem Solving
- Lesson 2: Angle-Angle (AA) and SAS in Geometric Proofs
  Module 2, Section 4, Lesson 2: Angle-Angle (AA) and SAS in Geometric Proofs

Section 5: Real-World Patterns and Structures
- Lesson 1: Analyzing Patterns in Nature with Congruence
  Module 2, Section 5, Lesson 1: Analyzing Patterns in Nature with Congruence
- Lesson 2: Practical Applications of Similarity in Design
  Module 2, Section 5, Lesson 2: Practical Applications of Similarity in Design


Module 3: Circle Fundamentals

Section 1: Circle Terminology and Definitions
- Lesson 1: Defining Circles, Radius, and Diameter
  Module 3, Section 1, Lesson 1: Defining Circles, Radius, and Diameter
- Lesson 2: Chords, Arcs, and Sectors Explained
  Module 3, Section 1, Lesson 2: Chords, Arcs, and Sectors Explained

Section 2: Circle Theorems – Part I
- Lesson 1: Understanding Central Angles and Inscribed Angles
  Module 3, Section 2, Lesson 1: Understanding Central Angles and Inscribed Angles
- Lesson 2: The Relationship Between Arcs and Angles
  Module 3, Section 2, Lesson 2: The Relationship Between Arcs and Angles

Section 3: Circle Theorems – Part II
- Lesson 1: Properties of Tangents and Secants
  Module 3, Section 3, Lesson 1: Properties of Tangents and Secants
- Lesson 2: Angle Relationships Involving Chords and Tangents
  Module 3, Section 3, Lesson 2: Angle Relationships Involving Chords and Tangents

Section 4: Measuring Circles
- Lesson 1: Calculating Circumference
  Module 3, Section 4, Lesson 1: Calculating Circumference
- Lesson 2: Determining the Area of a Circle
  Module 3, Section 4, Lesson 2: Determining the Area of a Circle

Section 5: Circle Constructions
- Lesson 1: Constructing Tangents to a Circle
  Module 3, Section 5, Lesson 1: Constructing Tangents to a Circle
- Lesson 2: Constructing Arcs and Angles with a Compass
  Module 3, Section 5, Lesson 2: Constructing Arcs and Angles with a Compass


Module 4: Polygons and Their Properties

Section 1: Introduction to Polygons
- Lesson 1: What Is a Polygon?
  Module 4, Section 1, Lesson 1: What Is a Polygon?
- Lesson 2: Classifying Polygons by Number of Sides
  Module 4, Section 1, Lesson 2: Classifying Polygons by Number of Sides

Section 2: Triangles and Their Properties
- Lesson 1: Different Types of Triangles
  Module 4, Section 2, Lesson 1: Different Types of Triangles
- Lesson 2: The Triangle Angle Sum Theorem
  Module 4, Section 2, Lesson 2: The Triangle Angle Sum Theorem

Section 3: Quadrilaterals and Other Four-Sided Figures
- Lesson 1: Properties of Parallelograms and Rectangles
  Module 4, Section 3, Lesson 1: Properties of Parallelograms and Rectangles
- Lesson 2: Exploring Squares and Rhombuses
  Module 4, Section 3, Lesson 2: Exploring Squares and Rhombuses

Section 4: Regular Polygons
- Lesson 1: Defining Regularity in Polygons
  Module 4, Section 4, Lesson 1: Defining Regularity in Polygons
- Lesson 2: Calculating Interior Angles in Regular Polygons
  Module 4, Section 4, Lesson 2: Calculating Interior Angles in Regular Polygons

Section 5: Real-World Applications of Polygons
- Lesson 1: Tessellations and Geometric Patterns
  Module 4, Section 5, Lesson 1: Tessellations and Geometric Patterns
- Lesson 2: Symmetry and Design in Polygons
  Module 4, Section 5, Lesson 2: Symmetry and Design in Polygons


Module 5: Introduction to Geometric Proofs

Section 1: Understanding the Structure of Proofs
- Lesson 1: What Is a Geometric Proof?
  Module 5, Section 1, Lesson 1: What Is a Geometric Proof?
- Lesson 2: The Two-Column Proof Format Explained
  Module 5, Section 1, Lesson 2: The Two-Column Proof Format Explained

Section 2: Logical Reasoning in Proofs
- Lesson 1: Fundamentals of Deductive Reasoning
  Module 5, Section 2, Lesson 1: Fundamentals of Deductive Reasoning
- Lesson 2: Avoiding Common Logical Fallacies
  Module 5, Section 2, Lesson 2: Avoiding Common Logical Fallacies

Section 3: Basic Theorem Proving
- Lesson 1: Proving the Triangle Angle Sum Theorem
  Module 5, Section 3, Lesson 1: Proving the Triangle Angle Sum Theorem
- Lesson 2: Proving Congruence Theorems in Triangles
  Module 5, Section 3, Lesson 2: Proving Congruence Theorems in Triangles

Section 4: Introduction to Indirect Proofs
- Lesson 1: The Concept of Proof by Contradiction
  Module 5, Section 4, Lesson 1: The Concept of Proof by Contradiction
- Lesson 2: Using the Contrapositive in Geometric Proofs
  Module 5, Section 4, Lesson 2: Using the Contrapositive in Geometric Proofs

Section 5: Practice and Creative Problem Solving
- Lesson 1: Guided Exercises in Geometric Proof
  Module 5, Section 5, Lesson 1: Guided Exercises in Geometric Proof
- Lesson 2: Developing Creative Strategies for Proofs
  Module 5, Section 5, Lesson 2: Developing Creative Strategies for Proofs