Geometry

Unit 1: Introduction to Geometry

• Introduction

• Geometric Building Blocks

• Lines and Basic Constructions

• Angles

• Circles and Arcs

Unit 2: Introduction to Proofs

• Introduction

• Algebra Review

• Introduction to Proofs

• Introduction to Lines and Angles Theorems

• Proof--Vertical Angle Congruency

Unit 3: Transformations

• Introduction

• Identify and Construct Transformations

• Proof--Angles

• Rotations in the Coordinate Plane

• Reflections Over One Line

• Reflections Over Two Lines

• Composition and Sequence of Transformations

• Proof--Parallel Lines

Unit 4: Congruence and Angle Relationships

• Introduction

• Compare Figures for Congruence

• Angle Relationships Formed by Parallel Lines

• Angle Relationships Formed by Perpendicular Lines

• Proof--Properties of Perpendicular Bisectors

Unit 5: Constructions--Lines and Angles

• Introduction

• Constructions--Copy and Bisect a Line and Angle

• Constructions--Perpendicular Lines and Bisector of a Line Segment

• Slope and Equations of Parallel and Perpendicular Lines

• Constructions--Parallel Line Through a Given Point

• Partition Line Segments into Ratios

Unit 6: Triangle Relationships

• Introduction

• Classifying Triangles

• Angle Bisectors

• Perpendicular Bisectors

• Medians and Altitudes

• Triangle Proofs Part 1

• Triangle Proofs Part 2

Unit 7: Congruent Triangles

• Introduction

• Triangle Sums

• Triangle Congruence Using SSS, SAS, ASA, and AAS

• Corresponding Parts of Congruent Triangles

• Properties of Equilateral Triangles

• Properties of Isosceles Triangles

Unit 8: Similarity

• Introduction

• Defining Similarity

• Ratios and Proportions

• Dilation By Scale Factor

• AA Similarity in Triangles

• Proofs--Similar Triangles

• Modeling With Similar Triangles

Unit 1: Right Triangle Trigonometry Part 1

• Introduction

• The Language of Trigonometry

• Special Right Triangles

• Solving For Sides

• Solving for Angles

Unit 2: Right Triangle Trigonometry Part 2

• Introduction

• Modeling With Right Triangles

• Sine and Cosine of Complementary Angles

• Applying the Pythagorean Theorem

Unit 3: General Triangle Trigonometry

• Introduction

• Prove the Law of Sines

• Prove the Law of Cosines

• Solving Triangles With Law of Sines

• Solving Triangles With Law of Cosines

• Area of a Triangle

Unit 4: Quadrilaterals

• Introduction

• Defining Quadrilaterals

• Prove Properties of Parallelograms Part 1

• Prove Properties of Parallelograms Part 2

• Solving Parallelograms

• Perimeter and Area in the Coordinate Plane

• Prove Rectangles in the Coordinate Plane

Unit 5: Circles

• Introduction

• Circle Definitions and Similarity

• Arc Length and Sector Area

• Relationships in Circles

• Equation of a Circle

• Proving Circles in the Coordinate Plane

Unit 6: Circle Constructions

• Introduction

• Segment Lengths and Circles

• Radians

• Inscribed and Circumscribed Circles of Triangles

• Constructions

• Proportionality in Circles

Unit 7: Volume

• Introduction

• Volume and Surface Area of Cylinders

• Volume of Cones and Pyramids

• Volume of Spheres

• Relating 2D and 3D Objects

• Parabolas

Unit 8: Modeling in Two and Three Dimensions

• Introduction

• Modeling Problem Toolbox

• Dissection Arguments and Cavalieri's Principle

• Simple Modeling Problems

• Complex Modeling Problems