The Ultimate Geometry Course
The Ultimate Geometry Course: this Effortless Math guide explains the topic in plain language, shows how it works through solved examples, and gives you free practice to try immediately, so the idea sticks instead of staying abstract.
Deciding what comes next? Read Is Algebra 2 harder than Geometry? and see the full order of math classes.
Geometry Study Course
The Ultimate Geometry Course brings the key topics into one organized review page, with lessons, worksheets, and practice links in one place.
TL;DR: A free Geometry course covering points, lines, angles, triangles, quadrilaterals, circles, similarity, congruence, transformations, surface area, volume, and coordinate geometry. Self-paced lessons with worked examples and free worksheets for every section.
Key takeaways:
- Covers all of high-school Geometry: shapes, proofs, similarity, transformations, circles, 3D solids, coordinate geometry.
- Each topic has a lesson plus a free worksheet with answer key.
- Designed for Geometry students in grades 9-10 and adult self-learners.
- Self-paced, one topic per day finishes the course in a school year; faster for reviewers.
- Free, no signup required.
If you want to take a completely free course that includes all you need to do well on the Geometry test, then this course is the one that will teach you every needed concept before the test date. It’s ideal for your needs and covers every Geometry concept. For education statistics and research, visit the National Center for Education Statistics.
This Geometry program as well as additional Effortless Math Education products gets utilized by multiple people taking the Geometry exam annually. It helps them review basic math info, as well as find out if they need to study more in certain math concepts. With it, you’ll get your best possible score on a Geometry examination. For education statistics and research, visit the National Center for Education Statistics.
Learn it all at your own speed, since there’s no required schedule! The lessons all include examples, special activities, notes, and practice sessions so you’ll totally understand it and learn all you need to know.
The Absolute Best Book to Ace Geometry
Geometry Complete Course
Geometric Tools and Concepts
- Points, Lines, and Planes
- Line Segments and Measurements
- Midpoint and distance
- Parallel Lines and Transversals
- Perpendicular Lines
- Lines, Rays, and Angles
- Types of Angles
- Complementary and Supplementary angles
- Bisecting an Angle
- Constructing a Triangle Given Its Sides
- The Circumscribed Circle
- The Inscribed Circle of a Triangle
- Inscribing Regular Polygons
Reasoning and Proofs
- Conjectures and Counterexamples
- Inductive Reasoning from Patterns
- Conditional Statements
- Logic and Truth Tables
- Converse, Inverse, and Contrapositive
- Biconditionals and Definitions
- Deductive Reasoning
- Properties of Equality and Congruence
- Two Column Proofs
- Proving Angles Congruent
Coordinate Geometry
- Finding Slope
- Writing Linear Equations
- Finding Midpoint
- Finding Distance of Two Points
- Finding a Graph’s Slope
- Graphing Lines Using Slope, Intercept Form
- Writing Linear Equations from Graphs
- Converting Between Standard and Slope-Intercept Forms
- Slope-intercept Form and Point-slope Form
- Write a Point-slope Form Equation from a Graph
- Writing Linear Equations From Y-Intercept and A Slope
- Comparison of Linear Functions: Equations and Graphs
- Equations of Horizontal and Vertical lines
- Graph a Horizontal or Vertical line
- Equation of Parallel and Perpendicular Lines
Transformations, Rigid Motions, and Congruence
- Transformations on the Coordinate Plane
- Transformations-rotations, reflections and translations
- Rotation on the Coordinate Plane
- Reflection on the Coordinate Plane
- Dilation on the Coordinate Plane
- Dilations: Finding the Scale Factor
- Dilations: Finding a Coordinate
- Translations on the Coordinate Plane
- Congruence and Rigid Motions
- Symmetries of a Figure
Quadrilaterals and Polygons
- Classifying Polygons
- Angles in Quadrilaterals
- Properties of Trapezoids
- Properties of Parallelograms
- Properties of Rectangles
- Properties of The Rhombus
- Properties of Squares
- Areas of Triangles and Quadrilaterals
- Perimeter of Polygons
- Polygons and Angles
Triangles
- Triangles
- Classifying Triangles
- Triangle Angle Sum
- Triangle Midsegment
- Angle Bisectors of Triangles
- Isosceles and Equilateral Triangles
- Right Triangles
- Special Right Triangles
- The Pythagorean Theorem
- Pythagorean Theorem Converse: Is This a Right Triangle?
- Geometric Mean in Triangles
- Exterior Angle Theorem
- Medians
- Centroid
- The Triangle Inequality Theorem
- SSS and SAS Congruence
- ASA and AAS Congruence
- HL Congruences
Dilation and Similarity
- Dilations
- Dilations and Angles
- Similarity
- Similarity Criteria
- Congruent and Similar Figures
- Area and Perimeter: Scale Changes
- The Side Splitter Theorem
- Similarity Transformations
- Partitioning a Line Segment
- Similar Polygons
- Right Triangles and Similarity
- Similar Solids
Trigonometry
- Pythagorean Identities
- Special Right Triangles
- Trigonometric Ratios
- Trig Ratios of General Angles
- Right-Triangle Trigonometry
- Trigonometry and the Calculator
- Inverse Trigonometric Ratios
- Solving Right Triangles
- Trigonometry and Area of Triangles
- Law of Sines
- Law Cosines
- Trigonometric Applications
Circle Geometry
- The Unit Circle
- Arc length and Sector Area
- Arcs and Central Angles
- Arcs and Chords
- Inscribed Polygons
- Inscribed Angles
- Tangents to Circles
- Secant Angles
- Secant-tangent and Tangent-tangent Angles
- Segment Lengths in Circle
- Segment Measures
- Standard Form of a Circle
- Finding the Center and the Radius of Circles
- Radian Angle Measurement
Surface Area and Volume
- Circumference and Area of a Circle
- Area of a Trapezoids
- Area of Polygons
- Nets of 3-D Figures
- Cubes
- Rectangular Prisms
- Cylinder
- Surface Area of Prisms and Cylinders
- Volume of Cones and Pyramids
- Surface Area of Pyramids and Cones
- Volume of Spheres
- Sphere Surface Area
- Solids and Their Cross Sections
- Volume of a Truncated Cone
Looking for the best resource to help you succeed on the Geometry test?
The Absolute Best Book to Ace the Geometry
Recommended EffortlessMath Books
For a workbook that pairs with this course, the Geometry for Beginners walks through every topic with worked examples and unit reviews. For complete prep with practice tests, see the Geometry Test Prep Bundle (resource currently unavailable).
Frequently Asked Questions
What is geometry class?
Geometry class is the high school math course about shapes, size, position and space. You study points, lines and angles, triangles and their congruence and similarity, quadrilaterals, circles, transformations, the Pythagorean theorem, surface area and volume, and coordinate geometry. Many classes also teach proofs, where you explain step by step why a statement must be true, for example why the angles of a triangle add up to 180°.
Is geometry class hard?
Geometry feels different from algebra rather than harder. It asks you to picture shapes, use diagrams and explain your reasoning, and some students find that refreshing while others find proofs challenging at first. Learning the vocabulary and key formulas early helps a lot, such as A = πr² for a circle and a² + b² = c² for right triangles. Practicing a few problems each day, with worked examples to check against, makes the course much more manageable.
Is geometry a high school course?
Yes. In the United States, geometry is usually a high school course, most often taken in 9th or 10th grade after Algebra 1. Some students take it in 8th grade on an accelerated track. Younger grades study basic geometry ideas like area, perimeter and angles, but the full course with congruence, similarity, circles and proofs is normally a high school class.
Is geometry a required class?
In many U.S. schools geometry is part of the standard math sequence needed to graduate, and colleges often expect to see it on a transcript. Requirements differ by state and district, though, so check your school’s graduation rules or ask a counselor. Even where it is optional, geometry topics such as area, volume and the Pythagorean theorem show up on the SAT, ACT and many state tests.
Can I take a geometry course online for free?
Yes. The Effortless Math geometry course is free and self-paced. Each topic has a lesson with worked examples and a free worksheet with an answer key. It works for students who want extra help with their school class, for summer review, or for adults relearning geometry. If you need official high school credit, though, check with your school, because a free review course does not usually give credit on its own.
What does a geometry course outline include?
A typical geometry course outline starts with the basic tools: points, lines, planes and angle relationships. It then covers triangles (congruence, similarity, the Pythagorean theorem and right-triangle trigonometry), quadrilaterals and polygons, and circles with arcs, chords and sectors. It finishes with transformations, coordinate geometry, and the surface area and volume of solids like prisms, cylinders, cones and spheres. Doing one topic a day makes it easy to pace yourself.
Related EffortlessMath Lessons
If a topic on this page feels rusty, these short lessons go deeper:
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