The properties of triangles connect trigonometric functions to geometric quantities like sides, angles, areas, and radii. The three fundamental laws — sine rule, cosine rule, and projection formula — relate sides and angles. The area can be expressed in multiple equivalent forms depending on the given data. The four key radii — circumradius R, inradius r, and three exradii r1, r2, r3 — have interrelationships through the area and semi-perimeter. Half-angle formulas express sin$\frac{A}{2}$, cos$\frac{A}{2}$, and tan$\frac{A}{2}$ in terms of sides only. These tools collectively allow solving any triangle problem: given any three independent pieces of information about a triangle, all other quantities can be determined.