Geometry
About this free Geometry course
Geometry is a free high school geometry course that unlocks the secrets of shapes and space. It covers the angles, symmetry, logic, and proofs at the heart of a standard Geometry class, starting with the tools of geometry: distance, midpoints, angles, and polygons.
From there, it builds up to writing proofs about lines, triangles, and quadrilaterals, with plenty of diagrams and challenges along the way. Every chapter ends with a chapter review and an answer key, so students can test themselves before moving on and teachers can use the reviews as ready-made practice sets.
Who this course is for
This course is designed for students in grades 8 through 10 taking high school geometry. You should be comfortable with Algebra 1 skills such as solving equations and working with slope, since many geometry problems use them.
Course outline
- Tools of geometry. Distance and midpoint formulas, angle types and pairs, 2D and 3D figures, and surface area and volume.
- Reasoning and proof. Inductive and deductive reasoning, truth tables, conditional statements, postulates, and algebraic and geometric proofs.
- Parallel and perpendicular lines. Transversals and angle pairs, slope, equations of lines, proving lines parallel, and distance from a point to a line.
- Congruent triangles. Classifying triangles, the Triangle Angle-Sum Theorem, SSS, SAS, ASA, and AAS, and isosceles and equilateral triangles.
- Similarity. Similar polygons, dilations, proving triangles similar, and the Triangle Proportionality (Side Splitter) Theorem.
- Relationships in triangles. Bisectors, medians, altitudes, circumcenter, incenter, centroid, triangle inequalities, and indirect proof.
- Quadrilaterals. Interior and exterior angle sums, parallelograms, rectangles, rhombi, squares, trapezoids, and kites.
What you'll learn
- Use distance, midpoint, and slope to solve coordinate geometry problems
- Write two-column, paragraph, and algebraic proofs
- Prove triangles congruent or similar using the standard postulates and theorems
- Identify the points of concurrency in a triangle and apply triangle inequalities
- Classify quadrilaterals and use their properties to find missing measures
How long it takes
Plan on about 25 hours: four hours or so per chapter, including the chapter review. Proof-heavy chapters take longer, so give yourself extra practice time there.
Frequently asked questions about Geometry
Is Geometry really free?
Yes. Geometry is completely free, with no fees, subscriptions, or account required. STEM for Others is a 501(c)(3) nonprofit, and every course in our curriculum library is free for students, families, and teachers.
Does the course teach geometry proofs?
Yes. Proofs are a major focus. You'll learn the logic behind them, then write algebraic, paragraph, and two-column proofs about angles, parallel lines, and triangles, and you'll finish with indirect proof.
How do I start the course?
Click Begin Course at the top of this page to open the full slide deck in a new tab. You can also flip through the slides embedded above. Work through one unit at a time and try the practice questions before moving on.
Do I get a certificate?
The self-paced Geometry materials don't include an official certificate. If you're taking the course through a STEM for Others chapter program, ask your chapter leader about recognizing your completion.
Can teachers and clubs use this curriculum?
Yes. Teachers, homeschool families, libraries, and after-school clubs are welcome to use the Geometry materials with their students at no cost. STEM for Others volunteers also teach our curriculum in partner schools and libraries. You can find a chapter near you or start one at your school.
