- Ch. 1Triangles: Basic Concepts and PropertiesWhen do three sticks make a triangle? Why do the angles always add to 180°?
- Ch. 2Triangle Area and Side–Angle TheoremsSame height? Area ratio = base ratio. Shared side? Compare another segment.
- Ch. 3Congruent TrianglesCongruent means one triangle can be moved exactly onto the other.
- Ch. 4Similar TrianglesSimilar = congruent plus scaling. Sides × k, angles unchanged, area × k².
- Ch. 5Theorems on Proportional Segments in a TriangleAngle bisector, Ceva, Menelaus. Three ratios multiply to 1, by area.
- Ch. 6The Four Centers of a TriangleFour centers in one triangle. Which can leave it? Which stay in a line?
- Ch. 7Triangles Inscribed in a TriangleShortest triangle with a vertex on each side? Unfold it into a ray of light.
- Ch. 8Right TrianglesSlide four triangles and c² becomes a² + b²: a right angle is an equation.
- Ch. 9Isosceles TrianglesEqual legs make the apex bisector, median and altitude one line, the axis.
- Ch. 10Equilateral TrianglesTwo gifts: a constant sum of distances, and 60° turns that join segments.
- Ch. 11Quadrilaterals: Basic Concepts and PropertiesAngles add up to 360°, and the side midpoints always form a parallelogram.
- Ch. 12ParallelogramsTwo pairs of parallel sides: equal sides, equal angles, diagonals that bisect.
- Ch. 13Rectangles and RhombusesIt is all in the diagonals: equal for a rectangle, perpendicular for a rhombus.
- Ch. 14SquaresTurn a square 90° and it fits itself. Rotate a corner across to join segments.
- Ch. 15TrapezoidsOnly one pair of sides is parallel. Slide a leg or a diagonal to simplify it.
- Ch. 16Cyclic and Tangential QuadrilateralsCyclic: opposite angles add to 180°. Tangential: opposite sides, a + c = b + d.