What is Geometry?

Geometry is a branch of mathematics involving measurement, properties, and relationships of figures and spaces. The term geometry comes from the Greek words geo and metry for Earth and measurement, respectively. Geometry has various real-world applications, from construction and architecture to biology, arts, and animation. As one of the oldest branches of mathematics, geometry concepts were developed to solve problems involving land wealth, surveying, and astronomy. The study of geometry includes topology, trigonometry, algebraic geometry, and differential geometry. Like much of mathematics, geometry is interconnected with other branches of math. Geometry and algebra are both essential for concepts such as parallel lines and angle measurements. Geometry and probability are central in measuring sample spaces.

Geometry is a core element in comprehensive mathematics education. Students in preschool begin exploring skills and concepts in geometry. Beginner geometry concepts include a study of lines, angles, and polygons. Students learn how to calculate the area, perimeter, and volume of figures. Students also explore pi and circles. Secondary-level geometry courses explore the Pythagorean Theorem and its applications to right angles and distances. Typical high school geometry courses also introduce inductive and deductive reasoning and geometric proofs. An introductory college course in geometry consists of an overview of the measurement of two-dimensional and three-dimensional figures, theorems, axioms, and postulates.

Geometry skills and concepts are embedded in every grade level in most math curricula in the United States, with a specific course in high school. Technical vocabulary is essential in geometry, so including geometry definitions is vital in any instructional resource.

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Geometry Topics

Algebraic geometry

Learn about algebraic geometry and the connection between algebra and geometry. Explore algebraic geometry notes and concepts and study examples of algebraic shapes.

Analytic geometry

Learn about analytic geometry. Trace the history of analytic geometry, identify key topics and formulas for analytic geometry, and discover examples of proofs.


Discover the circle shape. Read the definition of what a circle is, study the parts of a circle, and study the mathematical formulas used to understand circles.

Convex geometry

Learn the convex geometry definition and how it works. Explore convex shapes and convex algebraic geometry and compare the meanings of concave and convex.

Euclidean geometry

This lesson introduces Euclidean Geometry. It details the history and development of Euclid's work, its concepts, statements, and examples.

Geometric measurement

Review geometry and measurement and how they are connected. Explore the basics of geometry and geometry concepts, and see how geometry and measurement are used.

History of geometry

Discover who invented geometry and why geometry is important in daily life. Learn about the origin of geometry. See the historical applications of geometry.


Learn about polygons and see examples of polygons. Discover how to find angles in polygons and the difference between regular polygons and irregular polygons.


What is symmetry in math? Learn about the line of symmetry definition and different lines of symmetry. Also learn about the four types of symmetry in math: reflection, rotation, point, and glide symmetry.

Transformation (function)

Explore transformations in mathematics. Learn the different types of transformations found in math and study various examples of each type of transformation.

Triangle geometry

What are the different types of triangles? Learn the definition of a triangle, how to identify the types of triangles, and see the parts of a triangle.


Learn the definition of a triangle in geometry. Learn about the parts of triangles and different types of triangles. Discover how to find the area of a triangle.

Geometry Resources

Study.com offers thousands of learning resources for math topics, including geometric shapes, properties in geometry, and geometric proofs. Use our resources as a full or supplemental curriculum for learning about geometric figures and geometry properties. Study.com's expert geometry instructors and tutors provide clear, step-by-step explanations to help students master various geometry types.

Geometry Courses

Study.com's collection of geometry courses includes an introduction to geometry, basic geometry, and advanced geometry. Learners strengthen their geometry knowledge using comprehensive lessons, review games, and practice tests.

Geometry Test Prep for Teachers and Students

Geometry Test Prep

Study.com offers math test-prep courses that cover geometry as well as other math topics. Younger students can review basic geometry as they prepare for the ISEE exam. Prospective teachers will appreciate the review of more advanced geometry and mathematical concepts as they study for their licensure tests. These review courses cover all the important topics that will be on the individual tests and are designed to be easy to use and learn from.


For teachers and parents

Geometry Lesson Plans for Teachers

Teachers can choose from over 200 time-saving geometry lessons in Study.com's library. Our resources focus on six overarching geometry topics. Choose from a collection of videos, practice materials, and assessments and track student progress using Study.com's teacher dashboard.

Lesson plans
  • Geometry Resources & Lesson Plans

    Our resources are suitable for individual and group learning, and focus on six overarching geometry topics: basic geometry, graphing and plotting, triangles, angles, polygons and quadrilaterals, and pi and circles.

Geometry Skills and Practice

Study.com's Geometry Skills and Practice section offers student and teacher resources for high school and college geometry. Whether students are learning about geometric properties, the Pythagorean Theorem, or logic and proofs, Study.com's expert instructors provide in-depth explanations and examples to support learners at all levels. Our library includes thousands of geometry practice problems designed to help students learn and master elementary and advanced concepts.

Teachers save time on curriculum planning with access to lessons, activities, practice tests, and assessments. Using our discussion questions and extension activities, teachers can build students' conceptual understanding. Geometry teachers can view sample questions and instructional resources to aid lesson planning. Teachers can print lesson transcripts as a geometry study guide for test preparation. Study.com's geometry lesson plans and activities are organized by topic or standard. Teachers can sort by content standards for over 40 states and the District of Columbia. Lesson sidebars also show related math concepts for extra support. Geometry teachers can track student progress using our dashboard and gain insights on skills to revisit with individual students or a class. Study.com's integration with Google Classroom, Canvas, and Schoology allows seamless assigning with a click of a button. Teachers can schedule assignments and due dates.

Students can take control of their learning using Study.com's self-paced geometry lessons. Our geometry practice problems and video walkthroughs help learners develop geometry knowledge using illustrations, models, and real-world connections. Students can access definitions, geometry examples, and step-by-step explanations at any point during learning and practicing. Our geometry practice tests offer students immediate feedback and opportunities to review step-by-step answers for incorrect geometry questions. Students can access illustrated video lessons and personalized support to build their understanding and confidence in geometry.

Our college geometry resources help develop mastery of fundamental geometry skills and concepts for a typical introductory course. Students can access thousands of video walkthroughs, explanations, and practice problems. Study.com provides flexibility for busy college students by offering proctored final exams directly on the Study.com site. Geometry course transcripts can be requested and sent to any accredited school.

Explore our geometry collection for fun and standards-aligned learning materials.

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Geometry Homeschool Curriculum

Our High School Geometry: Homeschool Curriculum includes over 160 self-paced lessons. Homeschool students can view animated lessons, complete practice tests, and play review games to master geometry concepts. Parents and homeschool instructors can access Study.com's library of online geometry resources, assign materials, and monitor learner progress. With an average length of eight minutes, Study.com's lessons provide clear and concise information to help students learn key concepts.

Homeschool solutions
Father and son doing homework

Study.com is an excellent program that can help my children learn anything. The incredible library of videos is more than I could have ever hoped for.

Gloria H.

Frequently Asked Questions

  • What is a geometry example?

    One example of geometry is finding the area of a figure. Floor plans or blueprints are drawn up using the length and width of a space to determine the square footage.

  • What are three types of geometry?

    Three types of geometry are Euclidean geometry, non-Euclidean geometry, and topology. Euclidean geometry involves points, lines, and planes. This type of geometry is often used in architecture and related fields. Non-Euclidean geometry is the study of curves and is typically used in cosmology. Topology is the study of stretching and bending shapes and space.

  • What kind of math is geometry?

    Geometry is a branch of mathematics involving the study of shapes and spaces. It deals with the measurements, properties, and relationships of figures and space.