Our Curriculum › Math › 10th Grade
Geometry
A full year of Geometry: angles and proof, congruent and similar triangles, quadrilaterals, circles, area and volume, constructions and right-triangle trigonometry, plus a 10-day capstone and a large number of applied and explainer projects.
180 lessons
One a day for a school year
10 units
Each opens to its lessons
10-day capstone project
Plus 27 applied and explainer projects
Standards
Common Core high school math
What's taught, unit by unit
Points, lines, angles & proof basicsDays 1–10
Points, lines and planes, what a proof is, segment and angle addition, midpoints and bisectors, complementary, supplementary and vertical angles, two-column proofs, and parallel lines cut by a transversal.
- 1 · Points, Lines, and Planes
- 2 · Introducing Geometric Proof
- 3 · Segment Addition and Midpoints
- 4 · Angle Addition and Angle Bisectors
- 6 · Complementary and Supplementary Angles
- 7 · Vertical Angles and Linear Pairs
- 8 · Introducing Two-Column Proof Format
- 9 · Parallel Lines Cut by a Transversal
Plus 2 review days, not listed.
Rigid motions, congruence & trianglesDays 11–25
Translations, reflections and rotations on the coordinate plane, symmetry, congruence through rigid motions, angle sums, proving triangles congruent (SSS, SAS, ASA, AAS, HL), isosceles triangles, midsegments and the triangle inequality.
- 11 · Precise Definitions of Rigid Motions
- 12 · Representing Transformations on the Coordinate Plane
- 13 · Symmetry: When a Figure Maps Onto Itself
- 14 · Sequences of Rigid Motions, Congruence, and CPCTC
- 16 · The Triangle Angle Sum and Exterior Angle Theorems
- 17 · SSS and SAS Congruence
- 18 · ASA and AAS Congruence
- 19 · HL Congruence and Writing Triangle Congruence Proofs
- 21 · The Isosceles Triangle Theorem
- 22 · Triangle Midsegments
- 23 · Triangle Inequality Theorem
- 24 · Relating Angle and Side Measures in Triangles
Plus 3 review days, not listed.
Similarity, quadrilaterals & polygonsDays 26–40
Proving triangles similar (AA, SSS, SAS) and solving for missing sides, properties of parallelograms, rectangles, rhombi, trapezoids and kites, polygon angle sums, the distance formula, and proving shapes with coordinates.
- 26 · Introducing Similarity
- 27 · AA Similarity
- 28 · SSS and SAS Similarity
- 29 · Solving for Missing Sides Using Similarity
- 31 · Properties of Parallelograms
- 32 · Proving a Quadrilateral Is a Parallelogram
- 33 · Rectangles, Rhombi, and Squares
- 34 · Trapezoids and Kites
- 36 · Polygon Angle Sum Formulas
- 37 · Regular Polygons and Exterior Angles
- 38 · The Distance Formula
- 39 · Proving Figures Using Coordinate Geometry
Plus 3 review days, not listed.
CirclesDays 41–50
Parts of a circle, central and inscribed angles, tangent lines, arc length, sector area, and writing and graphing the equation of a circle.
- 41 · Parts of a Circle
- 42 · Central Angles and Arcs
- 43 · Inscribed Angles
- 44 · Tangent Lines to a Circle
- 46 · Arc Length
- 47 · Area of a Sector
- 48 · The Equation of a Circle
- 49 · Graphing Circles From Their Equations
Plus 2 review days, not listed.
Area, volume, constructions & probabilityDays 51–70
Where area formulas come from, composite figures, surface area and volume of prisms, cylinders, cones, pyramids and spheres, compass-and-straightedge constructions, and conditional probability with the addition rule.
- 51 · Deriving the Area Formulas for Triangles and Parallelograms
- 52 · Deriving the Area Formulas for Trapezoids and Regular Polygons
- 53 · Deriving the Area Formula for Circles
- 54 · Area of Composite Figures
- 56 · Deriving Surface Area by Unfolding a Prism's Net
- 57 · Deriving Surface Area by Unrolling a Cylinder
- 58 · Deriving Volume by Stacking Cross-Sections (Cavalieri's Principle)
- 59 · Cone, Pyramid, and Sphere Volume as Fractions of Prisms and Cylinders
- 61 · Introducing Compass and Straightedge Constructions
- 62 · Constructing a Segment Bisector
- 63 · Constructing an Angle Bisector
- 64 · Constructing a Perpendicular Line
- 66 · Constructing a Line Parallel to a Given Line
- 67 · Constructing an Equilateral Triangle
- 68 · Conditional Probability and Independence
- 69 · The Addition Rule and Compound Events
Plus 4 review days, not listed.
Right-triangle trigonometryDays 71–80
Sine, cosine and tangent, finding sides and angles, inverse trig ratios, angles of elevation and depression, multi-step problems, and measuring heights with a clinometer.
- 71 · Introducing Right Triangle Trigonometry
- 72 · The Sine Ratio
- 73 · The Cosine Ratio
- 74 · The Tangent Ratio
- 76 · Finding Missing Angles Using Inverse Trig Ratios
- 77 · Angles of Elevation and Depression
- 78 · Solving Multi-Step Right Triangle Problems
- 79 · Applying Trig Ratios to Real-World Measurement
Plus 2 review days, not listed.
Cumulative review, projects & practiceDays 81–120
Cumulative reviews of every topic, mixed review sets and timed practice, explainer projects and applied projects (room layout, scale model, packaging, art, navigation, sports, photography), and a second look at transformations, congruence and dilations.
- 81 · Cumulative Review: Foundations and Proof
- 82 · Cumulative Review: Triangle Congruence and Similarity
- 83 · Cumulative Review: Quadrilaterals and Polygons
- 84 · Cumulative Review: Circles
- 86 · Cumulative Review: Area, Surface Area, and Volume
- 87 · Cumulative Review: Constructions and Coordinate Geometry
- 88 · Cumulative Review: Right Triangle Trigonometry
- 89 · Practicing a Comprehensive Mixed Geometry Review Set 1
- 91 · Explainer Project: Teaching Triangle Congruence
- 92 · Explainer Project: Teaching Right Triangle Trig
- 93 · Real-World Synthesis Project: Designing a Room Layout
- 94 · Real-World Synthesis Project: Building a Scale Model
- 96 · Real-World Synthesis Project: Estimating Distant Heights
- 97 · Explainer Project: Teaching Circle Theorems
- 98 · Real-World Synthesis Project: Packaging Design
- 99 · Completing a Final Applied Geometry Project of Your Choice
- 101 · Introducing Rigid Motion Transformations
- 102 · Connecting Transformations to Congruence
- 103 · Connecting Dilations to Similarity
- 104 · Explainer Project: Teaching Transformations
- 106 · Applied Project: Geometry in Art and Architecture
- 107 · Applied Project: Geometry in Navigation and Mapping
- 108 · Practicing a Comprehensive Mixed Geometry Review Set 2
- 109 · Timed Practice Geometry Assessment
- 111 · Explainer Project: Teaching Area, Surface Area, and Volume Formulas
- 112 · Applied Project: Geometry in Sports
- 113 · Applied Project: Geometry in Photography and Design
- 114 · Reviewing Common Geometry Proof Errors
- 116 · Cumulative Review: A Year of Geometry (Part 1) — Proof, Congruence, Similarity, Quadrilaterals
- 117 · Cumulative Review: A Year of Geometry (Part 2) — Circles, Measurement, Constructions, Trig
- 118 · Reflecting on a Year of Geometric Thinking
- 119 · A Sneak Peek: What Comes After Geometry
Plus 8 review days, not listed.
Capstone projectDays 121–130
Ten days on one self-chosen geometry topic: choosing it, researching the geometry behind it, solving applied problems, making visuals, writing it up, and presenting to the family.
- 121 · Beginning the Capstone: Choosing a Geometry-in-the-World Topic
- 122 · Researching the Capstone's Geometric Foundations
- 123 · Solving Applied Problems for the Capstone
- 124 · Creating Visuals for the Capstone
- 126 · Writing Up the Capstone's Explanation
- 127 · Completing the Capstone Project
- 128 · Preparing to Present the Capstone
- 129 · Presenting the Capstone Project
Plus 2 review days, not listed.
Review, applied projects & timed practiceDays 131–170
Cumulative reviews of angles and proof, common-error days for circles and trigonometry, timed practice assessments, explainer projects, and applied projects such as city planning, bridges, astronomy, fashion, surveying, aviation and robotics.
- 131 · Cumulative Review: Angles and Triangle Fundamentals
- 132 · Cumulative Review: Proof Strategies
- 133 · Explainer Project: Teaching Coordinate Proof
- 134 · Applied Project: Geometry in City Planning
- 136 · Reviewing Common Errors in Circle Problems
- 137 · Timed Practice Assessment: Proof and Congruence
- 138 · Timed Practice Assessment: Measurement and Trig
- 139 · Mid-Late-Year Reflection: Geometry Progress
- 141 · Applied Project: Geometry in Video Game Design
- 142 · Applied Project: Geometry in Bridge Engineering
- 143 · Explainer Project: Teaching the Pythagorean Theorem's Applications
- 144 · Practicing a Comprehensive Mixed Geometry Review Set 3
- 146 · Applied Project: Geometry in Astronomy
- 147 · Applied Project: Geometry in Fashion Design
- 148 · Reviewing Common Errors in Trigonometry Applications
- 149 · Practicing a Comprehensive Mixed Geometry Review Set 4
- 151 · Applied Project: Geometry in Solar Panel Placement
- 152 · Applied Project: Geometry in Land Surveying
- 153 · Explainer Project: Teaching Similar Triangles
- 154 · Practicing a Comprehensive Mixed Geometry Review Set 5
- 156 · Applied Project: Geometry in Aviation Navigation
- 157 · Reviewing Common Errors in Circle Equations
- 158 · Practicing a Comprehensive Mixed Geometry Review Set 6
- 159 · Timed Practice Assessment: A Full-Year Mixed Set
- 161 · Applied Project: Geometry in Robotics
- 162 · Applied Project: Geometry in Furniture Design
- 163 · Explainer Project: Teaching Surface Area vs. Volume
- 164 · Practicing a Comprehensive Mixed Geometry Review Set 7
- 166 · Full-Year Geometry Cumulative Review, Part 1
- 167 · Full-Year Geometry Cumulative Review, Part 2
- 168 · Full-Year Geometry Cumulative Review, Part 3
- 169 · Timed Practice Assessment: The Comprehensive Final
Plus 8 review days, not listed.
Final review & celebrationDays 171–180
Final reviews of proof, congruence, similarity, circles, measurement and trigonometry, a year-end presentation, three celebration days, a roadmap for Algebra II, and a final reflection.
- 171 · Final Review: Proof, Congruence, and Similarity
- 172 · Final Review: Circles, Measurement, and Trigonometry
- 173 · Preparing Your Year-End Math Presentation
- 174 · Delivering Your Year-End Math Presentation
- 175 · Celebration Day: Reflecting on a Year of Geometry!
- 176 · Celebration Day: A Favorite Problem Challenge
- 177 · Celebration Day: Geometry All Around You
- 178 · Looking Ahead: Your Roadmap for Algebra II
- 179 · Final Reflection: My Year in Geometry
- 180 · Congratulations! You Completed Geometry 10!
By the end of the year, your child can
- Write two-column proofs about angles, parallel lines and triangles
- Prove triangles congruent or similar and use that to find missing measures
- Use properties of quadrilaterals, polygons and circles to find angles, arcs and lengths
- Find area, surface area and volume of common 2D and 3D figures
- Use sine, cosine and tangent to solve right-triangle problems
- Complete basic constructions with a compass and straightedge
Other 10th Grade subjects: English 10: Literature · English 10: Composition & Grammar · Chemistry · US History