Geometry is more than memorizing formulas. It is a way of thinking that helps you describe space with precision, reason from definitions, and justify conclusions step by step. In this free online course, you will develop a strong foundation in Euclidean geometry, starting with the language of points, lines, segments, rays, and circles, then moving into how mathematicians communicate ideas with clear notation and carefully defined terms.
As you progress, you will learn to see angles not just as measurements but as relationships. You will work with degrees and protractors, connect complementary and supplementary pairs, and recognize structures created by intersecting lines, parallel lines, and transversals. With guided practice, these patterns become tools you can use to find unknown measures and check your reasoning quickly and accurately.
A major focus is learning how geometry proves things, not just states them. You will encounter classic arguments such as why vertical angles are equal, why triangle angle sums work the way they do, and how angle relationships can establish parallelism. From there, you will strengthen your problem-solving with triangle congruence and similarity, understanding what information is sufficient to guarantee a match, why certain tempting shortcuts fail, and how to turn diagrams into logical evidence.
The course also connects geometry to real calculation. You will revisit perimeter and area with a deeper sense of where formulas come from, explore circles, pi, and sector-related ideas, and expand into volume and surface area for solids like prisms and cylinders. Along the way, special triangles and the Pythagorean theorem help bridge visual intuition with algebraic accuracy.
To round out your understanding, you will study key triangle centers and notable lines—ideas that reveal symmetry, balance, and structure in figures. With videos plus targeted exercises, you can practice until the concepts feel natural, preparing you for school exams, future STEM courses, or any situation where spatial reasoning and clear logical thinking matter.
Course content
Video class: Euclid as the father of geometry | Introduction to Euclidean geometry | Geometry | Khan Academy08m
Exercise: Who is considered the father of geometry due to his foundational work in the field?
Video class: Basic geometry: language and labels | Introduction to Euclidean geometry | Geometry | Khan Academy12m
Exercise: What is the primary meaning of 'geometry' based on its root words?
Video class: Intro to lines, line segments, and rays | Geometry | Khan Academy03m
Exercise: What is the pure geometrical definition of a ray?
Video class: Language and notation of the circle | Introduction to Euclidean geometry | Geometry | Khan Academy11m
Exercise: What is the definition of a circle according to the video?
Video class: Angle basics | Angles and intersecting lines | Geometry | Khan Academy06m
Exercise: How is an angle properly denoted in geometry?
Video class: Measuring angles in degrees | Angles and intersecting lines | Geometry | Khan Academy08m
Exercise: What is a protractor used for?
Video class: Measuring angles using a protractor | Angles and intersecting lines | Geometry | Khan Academy03m
Exercise: How do you measure an angle using a virtual protractor?
Video class: More angle measurements using a protractor | Angles and intersecting lines | Geometry | Khan Academy04m
Exercise: What is the typical use for a protractor when measuring angles?
Video class: Complementary and supplementary angles | Angles and intersecting lines | Geometry | Khan Academy08m
Exercise: _What is the term used for two angles that share the same side?
Video class: Introduction to vertical angles | Angles and intersecting lines | Geometry | Khan Academy07m
Exercise: What is the measure of angle CEB if angle BED = 70 degrees?
Video class: Proof: Vertical angles are equal | Angles and intersecting lines | Geometry | Khan Academy04m
Exercise: What can be concluded about vertical angles?
Video class: Angles formed by parallel lines and transversals | Geometry | Khan Academy07m
Exercise: What type of angles are formed by a transversal intersecting two parallel lines?
Video class: Proof - Sum of Measures of Angles in a Triangle are 18006m
Exercise: What is the sum of the interior angles of a triangle?
Video class: Triangle angle example 1 | Angles and intersecting lines | Geometry | Khan Academy06m
Exercise: What is the measure of the missing angle z in the triangle?
Video class: Triangle angle example 2 | Angles and intersecting lines | Geometry | Khan Academy04m
Exercise: What is the measure of angle x?
Video class: Triangle angle example 3 | Angles and intersecting lines | Geometry | Khan Academy05m
Exercise: What is the measure of angle theta in the triangle?
Video class: Challenging triangle angle problem | Angles and intersecting lines | Geometry | Khan Academy08m
Exercise: _What is the formula for finding the sum of the exterior angles of a polygon?
Exercise: Which triangles are congruent based on given criteria?
Video class: More on why SSA is not a postulate | Congruence | Geometry | Khan Academy07m
Exercise: Why is SSA not a valid triangle congruence postulate?
Video class: Congruent triangle proof example | Congruence | Geometry | Khan Academy05m
Exercise: Is point E the midpoint of segment BC?
Video class: Congruent triangle example 2 | Congruence | Geometry | Khan Academy12m
Exercise: _According to the given diagram and statements, which of the following is true?
Video class: Congruent legs and base angles of isosceles triangles | Congruence | Geometry | Khan Academy09m
Exercise: What can we conclude about an isosceles triangle?
Video class: Equilateral triangle sides and angles congruent | Congruence | Geometry | Khan Academy06m
Exercise: What is an equilateral triangle?
Video class: Equilateral and isosceles example problems | Congruence | Geometry | Khan Academy06m
Exercise: What is the measure of angle ABE in the triangle?
Video class: Another isosceles example problem | Congruence | Geometry | Khan Academy05m
Exercise: _What are the possible values of x in an isosceles triangle where one angle measures 3x + 5 degrees and the other angle measures x + 16 degrees?
Video class: Example involving an isosceles triangle and parallel lines | Congruence | Geometry | Khan Academy03m
Exercise: What is the value of x in the isosceles triangle?
Video class: Figuring out all the angles for congruent triangles example | Congruence | Geometry | Khan Academy04m
Video class: Perimeter and area: the basics | Perimeter, area, and volume | Geometry | Khan Academy08m
Exercise: What is the perimeter of a rectangle with sides 7 and 5?
Video class: Triangle area proofs | Perimeter, area, and volume | Geometry | Khan Academy10m
Exercise: _What is the formula for finding the area of a right triangle?
Video class: Interesting perimeter and area problems | Perimeter, area, and volume | Geometry | Khan Academy08m
Video class: Koch snowflake fractal | Perimeter, area, and volume | Geometry | Khan Academy09m
Exercise: What is a unique property of the Koch snowflake?
Video class: Area of an equilateral triangle | Perimeter, area, and volume | Geometry | Khan Academy03m
Exercise: How do you calculate the area of an equilateral triangle as a function of side length s?
Video class: Area of Koch snowflake (part 1) - advanced | Perimeter, area, and volume | Geometry | Khan Academy12m
Exercise: _What is the "coach" snowflake and how is it constructed?
Video class: Area of Koch snowflake (part 2) - advanced | Perimeter, area, and volume | Geometry | Khan Academy06m
Video class: Challenging perimeter problem | Perimeter, area, and volume | Geometry | Khan Academy09m
Video class: Similar triangle basics | Similarity | Geometry | Khan Academy09m
Exercise: What is the relationship between two triangles with equal corresponding angles and side lengths scaled by the same factor?
