1
Understand
Learn what the idea means and why mathematicians needed it.
HOW THIS COURSE TEACHES
Understanding comes before memorizing.
2
See It Work
Follow worked examples where every important step is explained.
3
Use It
Connect geometry to money, motion, science, construction, computers and everyday problems.
4
Practice
Work problems yourself with progressive hints when you need help.
5
Get Tutored
Ask the local AI tutor to explain anything another way.
6
Prove Mastery
Use practice tests and exams to find what you know and what needs review.
COMPLETE COURSE
Beginner Foundations → Advanced Geometry
Follow the course from Unit 1 or jump directly to a subject you are studying in school.
UNIT 1
Foundations of Geometry
Learn the language, ideas and reasoning that geometry is built on.
UNIT 2
Angles
Understand how turns and intersections are measured.
UNIT 3
Parallel and Perpendicular Lines
Explore line relationships and the patterns created by transversals.
UNIT 4
Triangles
Study one of the most important structures in mathematics and engineering.
UNIT 5
Congruent Triangles
Determine when two triangles must have exactly the same size and shape.
UNIT 6
Similarity
Understand shapes with the same form but different scale.
UNIT 7
Right Triangles
Use right triangles to measure distances that cannot be measured directly.
UNIT 8
Quadrilaterals
Understand rectangles, squares, parallelograms, rhombi, trapezoids and kites.
UNIT 9
Polygons
Study many-sided figures and the patterns connecting their angles.
UNIT 10
Perimeter and Area
Measure boundaries and the amount of surface inside two-dimensional shapes.
UNIT 11
Circles
Explore radius, diameter, circumference, area, arcs and sectors.
UNIT 12
Coordinate Geometry
Connect geometric figures with numbers and the coordinate plane.
UNIT 13
Transformations
Move and resize geometric figures while studying what remains unchanged.
UNIT 14
Three-Dimensional Geometry
Measure and reason about solid objects in the real world.
UNIT 15
Proof, Construction and Applied Geometry
Bring the course together through reasoning, construction and real applications.
PRACTICE LAB
Practice until it makes sense.
New problems are generated automatically. Wrong answers can receive hints instead of immediately revealing the answer.
Press “New Problem” to begin.
Practice Exam
Generate a comprehensive 30-question Geometry practice exam covering the course.
LOCAL AI TUTOR
Ask “why?” as many times as you need.
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WHERE DID GEOMETRY COME FROM?
Geometry has a story.
Mathematics did not suddenly appear in a textbook. People developed it over thousands of years because they had real problems they needed to solve.
Early practical geometry
Long before formal mathematical proof, ancient civilizations used geometric ideas for construction, surveying, astronomy and measurement.
Ancient Egypt
Egyptian mathematics included practical methods for measuring land, calculating areas and volumes, and planning large structures.
Babylonia
Babylonian mathematics included sophisticated numerical geometry, including calculations involving areas, triangles and relationships now associated with the Pythagorean theorem.
Greek geometry
Greek mathematicians developed geometry into a deductive system in which conclusions were established through definitions, assumptions and logical proof.
Euclid
Around 300 BCE, Euclid organized a large body of Greek mathematical knowledge in the Elements. Its axiomatic approach strongly influenced mathematics for more than two thousand years.
Later development
Mathematicians in India, China, the Islamic world and Europe continued developing geometric techniques, trigonometry, coordinate methods and new approaches to space.
Modern geometry
Geometry now includes coordinate, projective, differential and non-Euclidean geometries and is fundamental to engineering, physics, computer graphics, robotics, architecture and navigation.
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