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Geometry

The mathematics of shape, size and position. From triangles to circles, geometry trains your spatial thinking.

18 topics

  1. 01CirclesOne number — the radius — decides everything about a circle.Lesson 1 of 18
  2. 02Pythagorean TheoremThe rule hidden in every right triangle — the squares of the legs add up to the square of the hypotenuse.Lesson 2 of 18
  3. 03AnglesAn angle measures how far something opens up — from a 1° crack to a 359° swing.Lesson 3 of 18
  4. 04TrianglesThree sides, three angles, an angle sum of exactly 180° — the simplest and most rigid shape of all.Lesson 4 of 18
  5. 05QuadrilateralsFour sides, four angles, an angle sum of 360° — a family album from trapezoid to square.Lesson 5 of 18
  6. 06PerimeterThe distance around a shape — it decides how much fencing, framing and trim you need.Lesson 6 of 18
  7. 07SymmetryOne fold or one turn that lands a shape exactly on itself — that is the secret of symmetry.Lesson 7 of 18
  8. 08Solid ShapesFaces, edges, vertices — plus one formula by Euler that ties them all together.Lesson 8 of 18
  9. 09Angles in PolygonsCut any polygon into triangles and every angle sum falls right out — interior, regular, and the walking-around 360°.Lesson 9 of 18
  10. 10Congruence & SimilarityCongruent means same shape and same size; similar means same shape, different size — the secret lives in the scale factor.Lesson 10 of 18
  11. 11TransformationsSlide, flip, turn, scale — the four moves of geometry, and every one of them can be written in coordinates.Lesson 11 of 18
  12. 12Introduction to TrigonometryOne acute angle fixes the ratios of all three sides — sine, cosine and tangent turn angles into sides, and sides back into angles.Lesson 12 of 18
  13. 13Arcs & SectorsSlice a wedge off a circle — the arc takes a share of the circumference, the sector a share of the area, and the central angle sets the share.Lesson 13 of 18
  14. 14Parallel Lines & TransversalsA third line slicing through two parallels creates eight angles of only two sizes — the F, Z and C shapes tell you which is which.Lesson 14 of 18
  15. 15Points, Lines and PlanesA dot from a pen tip, a stretched string, a tabletop — the three basic building blocks of geometry.Lesson 15 of 18
  16. 16Circle TheoremsThree angle theorems about central angles, inscribed angles and diameters — the rules a circle quietly enforces.Lesson 16 of 18
  17. 17Trig Identitiessin and cos are not strangers — the Pythagorean theorem puts on algebraic clothes and becomes sin²θ + cos²θ = 1, true for every angle.Lesson 17 of 18
  18. 18Sine and Cosine RulesTriangles without a right angle can still be solved — the sine rule pairs each side with its opposite angle, and the cosine rule extends the Pythagorean theorem to any angle.Lesson 18 of 18

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