“Aristotle is so impressive. It explained a math problem to my daughter that ChatGPT couldn't figure out.”
Akshay
parent of Tara, 15
Grades 9–12Your child's own
Your child's own
world‑class geometry tutor
Pioneered by Stanford AI researchers and learning scientists, Aristotle is the world's first voice-based AI geometry tutor.
From first proofs through circles and trigonometry, Aristotle has improved thousands of grades over 22% within a week.
Trusted by families at
The curriculum
Over 190 geometry skills, personalized to your child
Aristotle is designed to always know what to teach at exactly the right time.
Sample curriculum
+ 9 more math subjects available
Not startedIn progressMastered* Click a topic to see the skills inside
* Click a topic to see the skills inside
Foundations of Geometry
Reasoning and Proof
Parallel and Perpendicular Lines
Transformations
Triangle Congruence
Relationships in Triangles
Quadrilaterals and Polygons
Similarity
Right Triangles and Trigonometry
Circles
Coordinate Geometry
Solid Geometry and Measurement
Probability
Geometry tutoring curriculum194 skills across 13 units
Foundations of Geometry
Lean on-ramp for the course: precise definitions and notation for points, lines, planes, segments, rays, and angles; segment and angle measurement and addition; coordinate midpoint and distance tools; angle pairs; and the core compass-and-straightedge tool constructions of the cross-cutting geo.construct.* family. Topics: Definitions and Notation, Segment Measurement, Angle Measurement, Angle Pairs, Coordinate Tools: Distance and Midpoint, Core Constructions.
Reasoning and Proof
Proof grammar practiced on easy content: conditional statements and their logical equivalents, inductive versus deductive reasoning, postulates and diagram conventions, and proof formats applied to algebraic, segment, and angle arguments. Topics: Conditional Statements and Logic, Proof Foundations and Formats.
Parallel and Perpendicular Lines
Transversal angle relationships and their proofs, criteria for proving lines parallel or perpendicular, and the coordinate side: slope criteria and equations of parallel and perpendicular lines, placed here with their conceptual basis ahead of the late Coordinate Geometry unit. Topics: Angles Formed by Transversals, Proving Lines Parallel, Perpendicular Lines, Slope Criteria and Equations of Lines.
Transformations
Rigid motions only: performing and describing translations, reflections, and rotations, the properties they preserve, compositions, symmetry, and congruence defined by rigid motions. Topics: Performing and Describing Rigid Motions, Compositions of Rigid Motions, Symmetry, Congruence via Rigid Motions.
Triangle Congruence
The first major synthesis: triangle angle theorems, congruence criteria (SSS, SAS, ASA, AAS, HL) justified by rigid motions, isosceles and equilateral triangle theorems, and congruence proofs with CPCTC. Topics: Triangle Angle Theorems, Congruence Criteria, Congruence Proofs.
Relationships in Triangles
Perpendicular and angle bisectors as loci, the four classical triangle centers, the midsegment theorem, and triangle inequality reasoning including the hinge theorem. Topics: Bisectors as Loci, Triangle Centers, Midsegments, Triangle Inequalities.
Quadrilaterals and Polygons
Polygon angle sums, parallelogram properties and proofs, special parallelograms, trapezoids and kites, and classification within the quadrilateral hierarchy. Topics: Polygon Angle Sums, Parallelograms, Rectangles, Rhombi, and Squares, Trapezoids and Kites, The Quadrilateral Hierarchy.
Similarity
The central relation changes from congruence to proportionality: dilations and their properties open the unit, then similarity defined via transformations, the AA/SSS/SAS criteria, proportionality theorems, and similar right triangles with geometric mean as the bridge into trigonometry. Topics: Dilations, Similar Figures and Criteria, Proportionality Theorems, Similar Right Triangles and Geometric Mean.
Right Triangles and Trigonometry
Pythagorean theorem and converse, special right triangles, and right-triangle trigonometry built on similarity, with elevation and depression applications. Topics: Pythagorean Theorem, Special Right Triangles, Right-Triangle Trigonometry, Trigonometry Beyond Right Triangles.
Circles
Central and inscribed angle relationships, chords, tangents, secants, segment products, circle proofs, arc length, sector area, and the radian connection, plus the circle constructions of the cross-cutting geo.construct.* family. Topics: Circle Vocabulary and Similarity, Angle and Arc Relationships, Chords, Tangents, and Segment Lengths, Circle Proofs, Arc Length, Sectors, and Radians, Circle Constructions.
Coordinate Geometry
The coordinate-methods unit: circle equations derived from the Pythagorean theorem, parabola focus and directrix work, partitioning directed segments, perimeter and area in the plane, and coordinate proofs that combine these tools with earlier figure properties. Topics: Equations of Circles, Parabolas from Focus and Directrix, Partitioning Segments, Coordinate Computations with Figures, Coordinate Proofs.
Solid Geometry and Measurement
Two-dimensional area including regular polygons and composites, cross sections and solids of revolution, volume formulas with informal derivations (including Cavalieri's principle), similar-solid scaling, and density and design modeling as the course's applications capstone. Topics: Area of Polygons and Composite Figures, Cross Sections and Solids of Revolution, Volume, Modeling with Geometry.
Probability
Conditional probability with sample spaces, events, independence, two-way tables, and the addition rule, plus geometric probability and counting methods as further extensions. Topics: Sample Spaces and Events, Independence and Conditional Probability, Geometric Probability and Counting.
From our families
What parents are telling us
“My son told me yesterday that we should cancel his human tutor, Aristotle is doing a better job. The human tutor was $250/hour.”
Kim
parent of Andy, 13
“Sam got an A+. So it def worked!!!”
Tina
parent of Sam, 14
Why families switch
Everything an hourly tutor can't be
On demand, 24/7
No scheduling, no weekly slot. Help is there during homework at 9pm and the morning before the test.
A fraction of the cost
Unlimited sessions on a flat plan instead of paying a human tutor by the hour.
Truly personalized
Aristotle tracks every skill your child has mastered and teaches at their exact frontier: never too easy, never too far ahead.
Driven by science
How Aristotle works
Dialogue over lectures
Your child speaks — the tutor listens and responds.
Interactive engagement is the highest level of learning · ICAP Framework
Misconceptions over mistakes
Finds the conceptual gap underneath the wrong answer.
Models the reasoning pattern, not just the error · MISTAKE
Expert-level error handling
Follows the same 3-step process expert tutors use.
Novice tutors skip to correction — experts don't · Bridge
Verified every turn
Every response is checked before it reaches your child.
Turn-by-turn verification improves outcomes · TRAVER
Gets them to think
Asks your child to explain, then guides them until they get there themselves.
Socratic dialogue outperforms GPT-4 by 12% · SocraticLM
Fits your child's geometry class
State, school, or home aligned curriculums
State standards
Every geometry skill is aligned to Common Core standards, including the transformations-based approach most schools now teach, so tutoring matches what your child is graded on.
Your child's school
Share the syllabus or textbook and sessions follow your child's actual class, whether that's public, private, or homeschool.
Your own goals
Working toward a placement exam, an honors class, or getting a grade up? Aristotle builds the path backwards from your goal.
FAQ
Common questions about online geometry tutoring
The full high school geometry sequence: 194 individually tracked skills across 54 topics, from foundations and proof through parallel lines, transformations, triangle congruence, similarity, right triangle trigonometry, circles, coordinate geometry, and solid geometry. Aristotle always knows which skills your child has mastered and what comes next, so every session picks up exactly where the last one ended.
Yes, and proofs are where most geometry students hit a wall. Aristotle works through proofs with your child on a shared whiteboard, asking them to explain each step out loud: what is given, what they need to show, and which theorem justifies the move. Proof skills build gradually: conditional statements and logic first, then two-column proofs about segments and angles, then congruence proofs with CPCTC, circle proofs, and coordinate proofs.
Your child talks through problems out loud while working with Aristotle on a shared whiteboard, whether that is marking up a diagram, finding a missing angle, or setting up a proof. Aristotle asks questions, listens to their reasoning, and guides them to the answer. Sessions start whenever your child is ready, with no scheduling: during homework at 9pm, or the morning before a test.
Algebra and geometry tutors charge $45 to $75 an hour, which comes to $540 to $900 a month at three hours a week. Aristotle costs $299 a month for unlimited sessions across every subject, or $49 for a single session.
Chatbots hand your child the answer and forget them when the chat ends. Aristotle teaches the way expert tutors do: it asks your child to explain their thinking, finds the misconception underneath a wrong answer, and guides them with questions until they can solve it themselves. It also carries the learning process across sessions, remembering what your child has mastered and planning what to teach next, like a personal tutor who never forgets.
Yes. Parents get a summary after every session, and the parent dashboard shows which skills your child has mastered and where they are stuck. Sessions are reviewed, and every tutor response is checked before it reaches your child.
Yes. Geometry struggles usually trace back to an earlier gap, sometimes in the algebra used to solve angle equations, sometimes in an earlier geometry skill like angle pairs that later theorems depend on. Each skill on the map is linked to its prerequisites, so Aristotle finds the exact earlier skill that is missing and rebuilds from there, instead of repeating the same lesson louder.
Aristotle teaches at your child's frontier, not their grade level. Honors classes move faster and lean harder on proofs, and Aristotle keeps pace, opening the next skill as soon as the current one is mastered. Accelerated students use sessions to work ahead of class, prepare for placement exams, or get a head start on Algebra 2.
Yes. The geometry course is aligned to Common Core standards, including the transformations-based approach to congruence and similarity that most schools now teach, and the tutor personalizes to your child's actual class. Share the syllabus, textbook, or upcoming test topics and sessions will follow what is happening in school.
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