Geometry Math Lessons
The Geometry course in 19 lessons, from Points, Lines, Segments and Angles to Geometric Modeling Applications, each one with its Key facts and a closing set of questions and answers.
- 81 US Letter pages
- 19 chapters
- 102 lesson sections
- PDF to print
- Cards accepted without a PayPal account
- Instant download, up to 3 devices
About this book
The Geometry course is built on transformations. The lessons go from points, lines and angles to rigid motions, congruent triangles and theorems about triangles, then to dilations, similarity and right triangle trigonometry.
Every chapter opens with the skills it builds; in Law of Sines and Law of Cosines, for instance: find the area of a triangle with two sides and the included angle, understand the Law of Sines, understand the Law of Cosines. A Key facts box sums up what to remember. Most of the 102 lesson sections of the book are written as questions a student would ask, such as What is the Law of Sines?
For a high school Geometry student, a parent, or a tutor who wants clear chapter material. Pair it with the Geometry Math Worksheets with Answers to practice each chapter right after reading it.
Detailed contents
The 19 chapters of the Geometry lesson book, the sections of each lesson and the page where each chapter starts.
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1
Points, Lines, Segments and Angles
- What are points, lines and planes?
- How do you find the length and midpoint of a segment?
- What is an angle and how do angles add?
- How is a circle defined?
- How do you solve a segment or angle problem with a variable?
- Basics lesson: questions and answers
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2
Translations, Reflections and Rotations
- What is a transformation?
- How does a translation work?
- How does a reflection work?
- How does a rotation work?
- How do you combine transformations?
- Geometry transformations lesson: questions and answers
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3
Symmetry of Polygons and Rigid Motions
- What is line symmetry?
- What is rotational symmetry?
- Why do rigid motions matter here?
- How do you find the symmetries of a polygon?
- Geometry symmetry lesson: questions and answers
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4
Congruent Triangles and Rigid Motions
- What does congruent mean?
- Which tests prove that two triangles are congruent?
- How do you decide whether two triangles are congruent?
- Congruence lesson: questions and answers
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5
Parallel Lines and Transversals
- What are vertical angles and linear pairs?
- What angles does a transversal make?
- What is a perpendicular bisector?
- How do you find an unknown angle?
- Parallel lines lesson: questions and answers
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6
Theorems About Triangles
- What is the triangle angle sum theorem?
- What is the exterior angle theorem?
- What do we know about isosceles triangles?
- What is a midsegment?
- What are medians and the centroid?
- Which side lengths make a triangle?
- Triangle theorems lesson: questions and answers
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7
Parallelograms and Quadrilaterals
- What is a parallelogram and what are its properties?
- What extra properties do special parallelograms have?
- What about kites and trapezoids?
- How do you find missing measures in a quadrilateral?
- Parallelograms lesson: questions and answers
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8
Geometric Constructions
- What tools are used in geometric constructions?
- How do you construct a perpendicular bisector?
- How do you bisect an angle?
- How do you construct an equilateral triangle, a square and a regular hexagon?
- Constructions lesson: questions and answers
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9
Dilations and Similarity
- What is a dilation?
- What does a dilation change and what does it keep?
- When are two figures similar?
- How do you solve a similarity problem?
- Dilations lesson: questions and answers
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10
Similar Triangle Theorems
- What does a line parallel to a side do to a triangle?
- How can you show triangles are similar?
- What happens in a right triangle with an altitude to the hypotenuse?
- How does similarity prove the Pythagorean theorem?
- How do you measure something you cannot reach?
- Similar triangles lesson: questions and answers
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11
Right Triangle Trigonometry
- What are the trigonometric ratios?
- How are sine and cosine of complementary angles related?
- How do you solve for a side or an angle?
- What are angles of elevation and depression?
- Right triangles lesson: questions and answers
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12
Law of Sines and Law of Cosines
- How do you find the area of a triangle with two sides and the included angle?
- What is the Law of Sines?
- What is the Law of Cosines?
- How do you solve a non-right triangle?
- Law of sines cosines lesson: questions and answers
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13
Circles: Angles, Chords and Tangents
- What are central and inscribed angles?
- What is true about an inscribed quadrilateral?
- What are the properties of tangents?
- What about chords, circumscribed circles and similarity?
- How do you solve a circle angle problem?
- Circle angles lesson: questions and answers
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14
Arc Length and Sector Area
- How do you find arc length?
- How do you find the area of a sector?
- What is a radian?
- How do you solve an arc or sector problem?
- Arcs sectors lesson: questions and answers
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15
Coordinate Geometry and Proofs
- How do slopes show parallel and perpendicular lines?
- How do you write the equation of a parallel or perpendicular line?
- How do you divide a segment in a given ratio?
- How do you find lengths, perimeter and area from coordinates?
- How do you prove a fact with coordinates?
- Coordinate geometry lesson: questions and answers
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16
Equations of Circles and Parabolas
- How is a circle written as an equation?
- Where are the center and the radius in the equation?
- Is a given point on the circle, inside it or outside it?
- What if the equation is not in center-radius form?
- How do a focus and a directrix define a parabola?
- Circle equations lesson: questions and answers
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17
Area, Volume and Dissection Arguments
- What are the circle formulas?
- How do you find the volume of a prism or a cylinder?
- What is Cavalieri's principle?
- How do you find the volume of a pyramid or a cone?
- What is the volume of a sphere?
- Geometry area volume lesson: questions and answers
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18
Cross Sections and Solids of Revolution
- What is a cross section?
- What are the cross sections of a cylinder?
- What are the cross sections of a cube and a cone?
- What is a solid of revolution?
- Geometry cross sections lesson: questions and answers
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19
Geometric Modeling Applications
- What does it mean to model an object with geometry?
- How do you use density?
- How do you solve a design problem with constraints?
- Modeling lesson: questions and answers
Sample pages
Three pages from the Geometry Math Lessons, exactly as you will print them. Click to enlarge.
How to use this lesson book
Read one chapter at a time
The 19 chapters follow the order of the Geometry course; at about 4 pages each, a chapter is one short sitting.
Copy the key facts
Write the Key facts of Coordinate Geometry and Proofs on an index card: a ready-made summary for the night before a quiz.
Try the closing questions
Cover the answers at the end of Geometric Modeling Applications and answer first: the best way to check understanding.
Frequently asked questions
What is in the Geometry lesson book?
81 US Letter pages and 19 chapters, one lesson per chapter, with 102 lesson sections in all. The full contents are listed above on this page.
Does the Geometry lesson book include exercises?
Each chapter ends with a short set of questions and answers. For full practice, the Geometry Math Worksheets with Answers follows the same 19 chapters.
Do I need the Geometry Math Worksheets with Answers along with the lesson book?
No, the Geometry Math Lessons stands on its own. But both books follow the same 19 chapters of Geometry; together they make a complete course, lesson then practice.
How do I receive the Geometry Math Lessons?
Right after paying with PayPal or a card, you reach your download page, where the Geometry Math Lessons is waiting. An email with the link is sent too.
Can I print the Geometry lesson book and open it on several devices?
Yes: the 81-page PDF of the Geometry Math Lessons prints as often as you need and opens on three devices (computer, tablet, phone). It carries your name at the bottom of the pages.
More answers on the shop page, or through our contact form.