Learn it in order

Start at a single point and build up to the angle rules that govern lines, triangles, and polygons.

1. Angles Around a Point
2. Complementary & Supplementary
3. Vertical Angles
4. Parallel Lines & Transversal
5. Triangle Angle Sum
6. Exterior Angle Theorem
7. Angle Sum of Polygons
8. Sum of Exterior Angles

Meet the four classic triangle centres, then the line and circle that tie them all together.

1. Incenter & Incircle
2. Circumcenter & Circumcircle
3. Centroid & the 2:1 Median
4. Orthocenter
5. Euler Line
6. Nine-Point Circle
7. Euler's Inequality

Where an angle's vertex sits — at the centre, on the circle, inside, or outside — decides everything.

1. Inscribed Angle Theorem
2. Tangent ⟂ Radius
3. Tangent–Chord Angle
4. Cyclic Quadrilateral
5. Intersecting Chords Angle
6. Intersecting Secants Angle
7. Tangent–Tangent Angle
8. Power of a Point

Every rigid motion of the plane is one of four kinds — reflect, rotate, translate, or glide — plus scaling.

1. Reflection
2. Rotation
3. Translation
4. Dilation (Scaling)
5. Two Reflections
6. Glide Reflection

Six different routes to the area of a shape — from side lengths and angles to counting lattice dots.

1. Heron's Formula
2. Triangle Area (sine)
3. Area = r·s
4. Area = abc/4R
5. Shoelace Formula
6. Pick's Theorem

Parallel lines split sides in equal ratios — and that one idea powers similar triangles and beyond.

1. Basic Proportionality
2. Triangle Midsegment
3. AA Similarity
4. SAS Similarity
5. Geometric Mean
6. Stewart's Theorem

From parallelograms to circle-inscribed quadrilaterals — the special quadrilaterals and their secrets.

1. Diagonals Bisect
2. Rhombus Diagonals
3. Parallelogram Law
4. Trapezoid Midsegment
5. Varignon's Theorem
6. Cyclic Quadrilateral
7. Pitot's Theorem
8. Ptolemy's Theorem
9. Brahmagupta's Formula

The right angle's special powers, ending with the law that generalises Pythagoras to any triangle.

1. Pythagorean Theorem
2. Geometric Mean
3. Median to Hypotenuse
4. Distance & Midpoint
5. British Flag Theorem
6. Law of Cosines