Geometry
Plane and solid geometry built on proof: reasoning and constructions, angles and parallel lines, rigid motions, congruence and similarity, right-triangle trigonometry, quadrilaterals and polygons, triangle centers, area, circles, coordinate geometry, solids, and geometric modeling, every result reasoned from first principles.
1. Foundations and Reasoning
- Points, Lines, and Planes
- Segments, Length, and Distance
- Angles and Their Measure
- Circles and Construction Tools
- Definitions, Conjectures, and Counterexamples
- Writing a Geometric Proof
2. Angles and Parallel Lines
- Angle Pairs
- Parallel Lines and Transversals
- Proving Lines Parallel or Perpendicular
- Angles in a Triangle
- The Exterior Angle Theorem
3. Rigid Transformations and Symmetry
Chapter Review A rapid pre-test review (speedrun) Chapter Test Questions from across the chapter4. Congruent Triangles
- Triangle Congruence and SSS
- SAS and ASA Congruence
- Isosceles and Equilateral Triangles
- AAS, HL, and Invalid Tests
- Using Congruence in Proofs
5. Geometric Inequalities
Chapter Review A rapid pre-test review (speedrun) Chapter Test Questions from across the chapter6. Similarity and Proportion
- Dilations and Scale Factors
- Similarity and AA
- SSS and SAS Similarity
- Triangle Proportionality and Midsegments
- The Angle-Bisector Ratio Theorem
- Applications of Similarity
7. Right Triangles and Trigonometry
- Similarity in Right Triangles
- The Pythagorean Theorem and Converse
- Special Right Triangles
- Sine, Cosine, and Tangent
- Solving Right Triangles
- Trigonometry in Measurement
8. Quadrilaterals and Polygons
- Classifying Polygons
- Polygon Angles and Tessellations
- Parallelograms
- Proving a Quadrilateral Is a Parallelogram
- Rectangles, Rhombi, and Squares
- Trapezoids and Kites
9. Triangle Centers and Constructions
- Perpendicular Bisectors and the Circumcenter
- Angle Bisectors and the Incenter
- Medians and the Centroid
- Altitudes and the Orthocenter
10. Perimeter and Area
- Area from Rectangles to Triangles
- Areas of Quadrilaterals
- Same Base, Same Height, and Area Ratios
- Areas of Regular Polygons
- Composite and Shaded Figures
- Area and Similarity
11. Circle Geometry
- Circles, Chords, and Arcs
- Tangents and Secants
- Inscribed Angles
- Cyclic Quadrilaterals
- Angles Inside and Outside Circles
- Segment Products and Power of a Point
12. Circle Measurement and Constructions
- Circumference and Circle Area
- Arc Length and Radians
- Sectors, Segments, and Circular Regions
- Inscribed Regular-Polygon Constructions
13. Coordinate Geometry
- Distance and Midpoint
- Partitioning a Segment
- Lines, Slopes, and Perpendicularity
- Coordinate Proofs and Polygon Measurement
- Equations of Circles
- Parabolas as a Distance Locus
14. Solid Geometry
- Solids, Nets, and Spatial Relationships
- Cross-Sections and Solids of Revolution
- Prisms and Cylinders
- Volumes of Pyramids and Cones
- Surface Areas of Pyramids and Cones
- Spheres and Hemispheres
- Composite and Hollow Solids
- Scaling in Three Dimensions
15. Geometric Modeling and Design
Chapter Review A rapid pre-test review (speedrun) Chapter Test Questions from across the chapter16. Further Geometry
- Generating Pythagorean Triples Advanced. This lesson goes beyond core Geometry. You can skip it.
- Triangle Area with Sine Advanced. This lesson goes beyond core Geometry. You can skip it.
- The Law of Sines Advanced. This lesson goes beyond core Geometry. You can skip it.
- The Law of Cosines Advanced. This lesson goes beyond core Geometry. You can skip it.
- Heron's Formula Advanced. This lesson goes beyond core Geometry. You can skip it.
- Coordinate Area Formulas Advanced. This lesson goes beyond core Geometry. You can skip it.
- Constructing Tangents from an External Point Advanced. This lesson goes beyond core Geometry. You can skip it.