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📐 Geometry
The mathematics of shape, size and position. From triangles to circles, geometry trains your spatial thinking.
- 01⭕CirclesOne number — the radius — decides everything about a circle.
- 02📐Pythagorean TheoremThe rule hidden in every right triangle — the squares of the legs add up to the square of the hypotenuse.
- 03📏AnglesAn angle measures how far something opens up — from a 1° crack to a 359° swing.
- 04🔺TrianglesThree sides, three angles, an angle sum of exactly 180° — the simplest and most rigid shape of all.
- 05⬛QuadrilateralsFour sides, four angles, an angle sum of 360° — a family album from trapezoid to square.
- 06🚧PerimeterThe distance around a shape — it decides how much fencing, framing and trim you need.
- 07🦋SymmetryOne fold or one turn that lands a shape exactly on itself — that is the secret of symmetry.
- 08🧊Solid ShapesFaces, edges, vertices — plus one formula by Euler that ties them all together.
- 09🔷Angles in PolygonsCut any polygon into triangles and every angle sum falls right out — interior, regular, and the walking-around 360°.
- 10👯Congruence & SimilarityCongruent means same shape and same size; similar means same shape, different size — the secret lives in the scale factor.
- 11🔄TransformationsSlide, flip, turn, scale — the four moves of geometry, and every one of them can be written in coordinates.
- 12📐Introduction to TrigonometryOne acute angle fixes the ratios of all three sides — sine, cosine and tangent turn angles into sides, and sides back into angles.
- 13🍕Arcs & 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.
- 14🛤️Parallel 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.
- 15⚫Points, Lines and PlanesA dot from a pen tip, a stretched string, a tabletop — the three basic building blocks of geometry.
- 16🎡Circle TheoremsThree angle theorems about central angles, inscribed angles and diameters — the rules a circle quietly enforces.
- 17🌀Trig Identitiessin and cos are not strangers — the Pythagorean theorem puts on algebraic clothes and becomes sin²θ + cos²θ = 1, true for every angle.
- 18🌉Sine 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.