The Geometry course teaches the properties and applications of common geometric figures in two and three dimensions. Geometry also emphasizes the ability to reason logically and critically. Students learn logical reasoning through the development of formal proofs throughout the Geometry course. Geometric properties of both two and three dimensions are emphasized as they apply to points, lines, planes, circles and polygons. Geometry Topics include: (1) Defining Geometric Figures and Shapes, (2) Logical Reasoning, (3) Properties of Lines in a Plane, (4) Triangles, (5) Quadrilaterals, (6) Circles, (7) Three-Dimensional Shapes, and (8) Surface Area and Volume.

- Definition of Space (Points, Lines, and Planes)
- Coordinate Plane Overview
- Collinear/Noncollinear and Coplanar/Noncoplanar
- The Intersection of Lines and Planes
- Postulates with Points, Lines, and Planes
- Measuring Segments
- Segment Addition Postulate
- Definition of a Midpoint
- Midpoint Formula
- Midpoint Theorem
- Segment Bisectors
- Pythagorean Theorem
- Distance Formula
- Introduction to Angles
- Measuring Angles
- Angle Bisectors
- Angle Addition Postulate
- Different Types of Angles (Acute, Right, and Obtuse)
- Angle Relationship Names (Adjacent, Vertical, and Linear Pairs)
- Vertical Angles and Linear Pairs
- Complementary and Supplementary Angles
- Definition of Congruent Angles and Congruent Segments
- Perpendicular Lines
- Geometric Notation

- Inductive Reasoning
- If-Then Conditional Statements
- The Converse of Conditional Statements
- Biconditional Statements
- The Negation of a Statement
- The Inverse and Contrapositive of a Conditional Statement
- Truth Tables for If-Then Conditional Statements
- Deductive Reasoning (Law of Detachment and Law of Syllogism)
- Different Types of Proofs
- An Introduction to Geometric Proofs
- Proving Algebraic Steps Using Algebraic Properties
- Theorems Involving Angle Relationships
- Introduction to Geometric Proofs with Angles
- Introduction to Geometric Proofs with Segments

- Definition of Parallel, Perpendicular, and Skew
- Lines with Transversals and Angles Formed
- Parallel Lines with Transversals and Angle Theorems
- Proving Angles Congruent
- Converse Theorems with Parallel Lines and Transversals
- Proving Lines are Parallel
- Perpendicular Transversal Theorem
- Parallel and Perpendicular Postulate
- Slopes of Parallel and Perpendicular Lines
- The Distance Between a Point and a Line

- Definition of a Triangle
- Classifying Triangles
- Angle Sum Theorem for Triangles
- Third Angle Theorem for Triangles
- Exterior Angles Theorem for Triangles
- Triangle Corollaries
- Congruent Triangles (CPCTC)
- Properties of Congruent Triangles (Reflexive, Symmetric, and Transitive)
- Side-Side-Side (SSS) Postulate
- Side-Angle-Side (SAS) Postulate
- Angle-Side-Angle (ASA) Postulate
- Angle-Angle-Side (AAS) Postulate
- Leg-Leg (LL) Theorem with Right Triangles
- Hypotenuse-Acute Angle (HA) and Leg-Acute Angle (LA) Theorems
- Hypotenuse Leg (HL) Theorem with Right Triangles
- Isosceles Triangle Theorem and Its Converse
- Equilateral Triangle Postulates

- Medians and Altitudes of Triangles
- Angle Bisectors of a Triangle
- Perpendicular Bisectors of a Triangle
- The Incenter of a Triangle
- The Circumcenter of a Triangle
- The Orthocenter and Centroid of a Triangle
- Exterior Angle Inequality Theorem for Triangles
- Angle-Side Correspondance Theorem for Triangles
- Shortest Distance from a Point to a Line
- Triangle Inequality Theorem
- Side-Angle-Side (SAS) Inequality Theorem (Hinge Theorem)
- Side-Side-Side (SSS) Inequality Theorem

- Properties of Quadrilaterals
- Properties of Parallelograms
- Four Theorems to Prove Quadrilaterals are Parallelograms
- Problems with Parallelograms
- Properties of Rectangles
- Problems with Rectangles
- Properties of Rhombi
- Problems with Rhombi
- Properties of Squares
- Problems with Squares
- Properties of Trapezoids
- Properties of an Isosceles Trapezoids
- Problems with Trapezoids
- Trapezoid Midsegment Theorem
- Properties of Kites

- Ratios and Proportions
- Similar Figures
- Angle-Angle (AA) Similiarity with Triangles
- Side-Side-Side (SSS) Similarity with Triangles
- Side-Angle-Side (SAS) Similiarity with Triangles
- Triangle Proportionality and Its Converse (Side Splitter Theorem)
- Parallel Lines and Transversal Proportionality
- The Triangle Midsegment Theorem
- Proportional Perimeters of Similar Figures
- Proportional Altitudes of Similar Triangles
- Proportional Angle Bisectors of Similar Triangles
- Proportional Medians of Similar Triangles
- Angle Bisector Proportionality Theorem
- Similarity within a Right Triangle

- The Geometric Mean between Two Numbers
- The Length of a Right Triangle's Altitude (Geometric Mean)
- The Length of a Right Triangle's Leg (Geometric Mean)
- Pythagorean Theorem
- Pythagorean Inequality Theorem
- Pythagorean Triples
- 45-45-90 Special Right Triangle
- 30-60-90 Special Right Triangles
- The Tangent Ratio of Right Triangles
- The Sine Ratio of Right Triangles
- The Cosine Ratio of Right Triangles
- How to use SOH-CAH-TOA
- Determining the Measure of a Angle Using Inverse Trig Ratios
- Angle of Elevation and Depression
- Law of Sines
- Law of Cosines

- Parts of a Circle
- Properties of Tangent Lines to a Circle
- Central Angles and Arcs
- Arcs and Chords
- Inscribed Angles
- Angle Relationships in Circles
- Segment Relationships in Circles
- Circles in the Coordinate Plane
- Circumference and Area of Circles
- Area of Sectors of Circles
- Area of a Segments of a Circle
- Arc Length

- Classifying Polygons
- Interior Angle Sum Theorem for Polygons
- Exterior Angle Sum Theorem for Polygons
- Area of Rectangles and Squares
- Area of Parallelograms
- Area of Triangles
- Area of Trapezoids
- Area of Rhombi
- Area of Kites
- Area of Regular Polygons
- Using Trigonometry to Find Area
- Area of Circles
- Area of Non-Regular Polygons
- Finding the Area of Shaded Region
- Perimeter and Area Ratios of Similar Figures
- Inscribed and Circumscribed Figures

- Exploring Solid Three-Dimensional Figures
- Cross Sections of Solid Three-Dimensional Figures
- Eurler's Formula
- Three Dimensional Distance and Midpoint Formulas
- Representations of Three-Dimensional Figures
- Nets of Three-Dimensional Figures
- Surface Area of Prisms and Cylinders
- Surface Area of Pyramids and Cones
- Volume of Prisms and Cylinders
- Volume of Pyramids and Cones
- Surface Area and Volume of Spheres
- Similar Solids