Geometry becomes much easier when you stop memorizing isolated facts and start seeing how ideas connect. This free online course is designed to help you build that connected understanding, moving from the basic language of geometry to the kinds of multi-step reasoning used in school exams and real problem solving. You will develop confidence working with points, lines, planes, segments, distance, and midpoint concepts, then use them as building blocks for angle measure and common angle relationships.
As you progress, the course emphasizes the habits that make geometry click: logical thinking, interpreting conditional statements, and forming valid arguments. Instead of treating proofs as a mystery, you will learn to justify steps clearly and recognize when a conclusion follows from a definition, a postulate, or a theorem. Along the way, practice activities reinforce what you learn so you can turn new concepts into reliable skills, not short-lived familiarity.
Coordinate geometry also plays an important role, connecting algebra and geometry through slope, equations of lines, and distance on the plane. You will learn to analyze parallel and perpendicular relationships and use them to solve problems efficiently. From there, the focus shifts to triangles and polygons, including classification, angle sum reasoning, congruence, and similarity. These topics help you reason about size and shape, compare figures, and apply proportional thinking to geometric situations.
The course continues into right-triangle tools such as the Pythagorean Theorem, special right triangles, and trigonometric ratios, supporting practical applications like angles of elevation and depression. You will also strengthen your understanding of circles through key relationships involving circumference, arcs, chords, inscribed angles, and tangents. Transformations such as reflections and translations tie many ideas together, helping you visualize movement and symmetry with clarity.
Whether you are catching up, getting ahead, or preparing for an exam, this course provides a structured path with guided instruction and targeted exercises. By the end, you will be better equipped to read geometry problems confidently, choose appropriate strategies, and explain your reasoning in a way that earns full credit.
Course content
Video class: 1-1 Point Line and Plane | Geometry | Ember Learning Labs18m
Exercise: In geometry, which of the following statements about a plane is true?
Video class: 1-2 Line Segments and Distance | Geometry | Ember Learning Labs17m
Exercise: In a given line segment AB, point C is on AB such that AC = 4x - 3 and CB = 2x + 5. If AB measures 19 units, what is the value of x?
Video class: 1-3 Midpoint Formula | Geometry | Ember Learning Labs13m
Exercise: What is the midpoint of the segment connecting the points (8, -2) and (-4, 6)?
Video class: 1-4 Angle Measure | Geometry | Ember Learning Labs25m
Exercise: In geometry, which type of angle is defined as an angle that measures exactly 90 degrees?
Video class: 1-5 Angle Relationships | Geometry | Ember Learning Labs16m
Exercise: Which pair of angles are considered supplementary angles?
Video class: 1-6 Two-Dimensional Figures | Geometry | Ember Learning Labs27m
Exercise: Which of the following statements accurately describes a polygon?
Video class: 1-7 Three-Dimensional Figures | Geometry | Ember Learning Labs23m
Exercise: Which of the following statements is true about a cylinder?
Video class: 2-1 Inductive Reasoning and Proof | Geometry | Ember Learning Labs15m
Exercise: In a sequence of numbers, the first term is 5, the second term is 11, and the third term is 17. If the sequence follows the same pattern, what would be the fifth term?
Video class: 2-2 Logic | Geometry | Ember Learning Labs24m
Exercise: What is the truth value of the compound statement 'not P or Q' when P is true and Q is false?
Video class: 2-3 Conditional Statements | Geometry | Ember Learning Labs19m
Exercise: In a conditional statement, which of the following describes the 'hypothesis' part?
Video class: 2-7 Proving Segment Relationships | Geometry | Ember Learning Labs18m
Exercise: Which of the following best describes the application of the segment addition postulate?
Video class: 2-8 Proving Angle Relationships | Geometry | Ember Learning Labs18m
Exercise: Which of the following statements is a correct interpretation of the vertical angles theorem?
Video class: 3-1 Parallel Lines and Transversals | Geometry | Ember Learning Labs15m
Exercise: In geometry, when dealing with parallel lines and a transversal, which pair of angles formed are considered alternate interior angles?
Video class: 3-2 Angles and Parallel Lines | Geometry | Ember Learning Labs12m
Exercise: If two parallel lines are cut by a transversal, which of the following statements is always true?
Video class: 3-3 Slopes of Lines | Geometry | Ember Learning Labs15m
Exercise: If line AB has a slope of 3, and line CD has a slope of -1/3, what can we conclude about lines AB and CD?
Video class: 3-4 Writing Equations of Lines | Geometry | Ember Learning Labs23m
Exercise: Which of the following represents the equation of a line that is parallel to the line y = 2x - 5?
Video class: Geometry Page 315 Number 10 walkthrough10m
Exercise: In a parallelogram, we have two sets of parallel lines. If XZ is the transversal line cutting these parallel lines and forms angles 1, 2, 3, and 4. If angle 1 is congruent to angle 3 and angle 2 is congruent to angle 4, which triangles formed by these lines can be proven congruent, and by which method?
Video class: 3-5 Proving Lines Parallel | Geometry | Ember Learning Labs10m
Exercise: When two lines are cut by a transversal and the pairs of alternate interior angles are congruent, what can we conclude about the lines?
Video class: 3-6 Perpendiculars and Distance | Geometry | Ember Learning Labs35m
Exercise: What is the distance between point A at (-2, 3) and point B at (4, -1) on a coordinate plane?
Video class: 4-1 Classifying Triangles | Geometry | Ember Learning Labs11m
Exercise: How can triangles be categorized based on their sides?
Video class: 4-2 Angles of Triangles | Geometry | Ember Learning Labs19m
Exercise: Using the Triangle Angle Sum Theorem, what is the measure of the third angle in a triangle if two of its angles are 65° and 75°?
Video class: 4-3 Congruent Triangles | Geometry | Ember Learning Labs10m
Exercise: Which of the following statements best describes congruent polygons?
Video class: 4-4 Proving Triangles Congruent SSS and SAS | Geometry | Ember Learning Labs12m
Exercise: Which of the following theorems can be used to prove that two triangles are congruent by knowing that two sides and the included angle are the same in both triangles?
Video class: 4-5 Proving Triangles Congruent ASA and AAS| Geometry | Ember Learning Labs11m
Exercise: Which of the following methods cannot be used to prove the congruence of triangles?
Video class: 4-6 Isosceles and Equilateral Triangles | Geometry | Ember Learning Labs07m
Exercise: Which of the following statements is true about equilateral triangles?
Video class: 5-1 Bisectors of Triangles | Geometry | Ember Learning Labs21m
Exercise: What is the circumcenter of a triangle?
Video class: 5-2 Medians and Altitudes of Triangles | Geometry | Ember Learning Labs17m
Exercise: What is the point of concurrency of the altitudes of a triangle called?
Video class: 5-3 Inequalities in One Triangle | Geometry | Ember Learning Labs08m
Exercise: According to the Exterior Angle Inequality Theorem, which of the following statements is true about the exterior angle of a triangle?
Video class: 5-4 The Triangle Inequality | Geometry | Ember Learning Labs06m
Exercise: Given three side lengths, determine which set can form a triangle based on the Triangle Inequality Theorem.
Video class: 5-6 Inequalities in Two Triangles | Geometry | Ember Learning Labs13m
Exercise: According to the hinge theorem, if two triangles have two pairs of congruent sides and one triangle has a larger included angle than the other, what can be said about their third sides?
Video class: 6-1 Angles of Polygons | Geometry | Ember Learning Labs16m
Exercise: In a hexagon, how many triangles can you create by connecting vertices from a single vertex?
Video class: 6-2 Parallelograms | Geometry | Ember Learning Labs12m
Exercise: Which of the following statements about parallelograms is true?
Video class: 6-3 Tests for Parallelograms | Geometry | Ember Learning Labs39m
Video class: 7-1 Ratios and Proportions | Geometry | Ember Learning Labs08m
Exercise: In a triangle, the sides are in the ratio of 3:4:5. If the shortest side is 9 units long, what is the length of the longest side?
Video class: 7-2 Similar Polygons | Geometry | Ember Learning Labs17m
Exercise: Two hexagons are similar. If the side lengths of the smaller hexagon are each 4 units and the side lengths of the larger hexagon are each 6 units, what is the scale factor from the larger hexagon to the smaller hexagon?
Video class: 7-3 Similar Triangles| Geometry | Ember Learning Labs30m
Exercise: Which theorem can be used to prove that two triangles are similar if you know that two angles in one triangle are congruent to two angles in another triangle?
Video class: 7-4 Parallel Lines and Proportional Parts | Ember Learning Labs23m
Exercise: Which theorem explains that if a line is parallel to one side of a triangle and intersects the other two sides, it divides the two sides into proportional segments?
Video class: 7-5 Parts of Similar Triangles | Ember Learning Labs26m
Exercise: If two triangles are similar, which of the following statements about their angle bisectors is true?
Video class: 7-6 Similarity Transformations | Ember Learning Labs28m
Exercise: What type of transformation ensures that two figures are similar, and what does this transformation involve?
Video class: 7-7 Scale Drawings and Models | Ember Learning Labs08m
Exercise: When working with scale factors in geometry, what must always be true about the units if you are converting a scale factor into a unitless scale?
Video class: 8-1 Geometric Mean | Ember Learning Labs19m
Exercise: In a right triangle, if an altitude is drawn to the hypotenuse, which of the following statements about the two triangles formed is correct?
Video class: 8-2 The Pythagorean Theorem and its Converse | Ember Learning Labs13m
Exercise: Which of the following sets of numbers is a Pythagorean triple?
Video class: 8-3 Special Right Triangles | Ember Learning Labs15m
Exercise: In a 45-45-90 triangle, if one of the legs has a length of 8 units, what is the length of the hypotenuse?
Video class: 8-4 Trigonometry | Ember Learning Labs28m
Exercise: In a right triangle, if the measure of angle A is 40°, which trigonometric function would give you the ratio between the side opposite angle A and the hypotenuse?
Video class: 8-5 Angles of Elevation and Depression | Ember Learning Labs29m
Exercise: A surveyor is measuring the height of a large building. She stands 100 feet away from the building and measures the angle of elevation to the top of the building to be 45°. How tall is the building, assuming her theodolite (measuring device) is at a height of 5 feet from the ground?
Video class: 8-6 The Laws of Sines and Cosines | Ember Learning Labs25m
Exercise: In geometry, which of the following is true about the Law of Sines when applied to a non-right triangle?
Video class: 8-7 Vectors | Ember Learning Labs25m
Exercise: Which of the following statements correctly describes a vector?
Video class: 9-1 Reflections | Ember Learning Labs13m
Exercise: When reflecting a triangle over a line x = -4, which of the following is true about the reflected image?
Video class: 9-2 Translations | Ember Learning Labs07m
Exercise: What happens to a figure when it is translated along a vector in a coordinate plane?
Video class: 10-1 Circles and Circumference | Ember Learning Labs07m
Exercise: What is the relationship between the circumference of a circle and its diameter?
Video class: 10-2 Measuring Angles and Arcs | Ember Learning Labs18m
Exercise: What is the arc length of an arc subtended by a 60-degree central angle in a circle with a radius of 5 cm?
Video class: 10-3 Arcs and Chords | Ember Learning Labs09m
Exercise: In a circle, if a diameter is perpendicular to a chord, what does it do to the chord and its corresponding arc?
Video class: 10-4 Inscribing Angles | Geometry | Ember Learning Labs15m
Exercise: What is the measure of an inscribed angle in a circle if the measure of its intercepted arc is 80 degrees?
Video class: 10-5 Tangents | Geometry | Ember Learning Labs09m
Exercise: What is a property of a tangent to a circle?
This free course includes:
15 hours and 57 minutes of online video course
Digital certificate of course completion (Free)
Exercises to train your knowledge
100% free, from content to certificate
Ready to get started?Download the app and get started today.
