By sides: equilateral (all equal), isosceles (two equal), scalene (all different). By angles: acute (all below 90°), right (one at 90°), obtuse (one above 90°). All interior angles sum to 180°.
a/sin(A) = b/sin(B) = c/sin(C). Used when you know two angles and a side (AAS/ASA) or two sides and a non-included angle (SSA).
c² = a² + b² − 2ab·cos(C). Used when you know two sides and the included angle (SAS) or all three sides (SSS). For right triangles it reduces to the Pythagorean theorem.
Area = ½ × base × height. When height is unknown use Heron's formula: √(s(s−a)(s−b)(s−c)) where s = (a+b+c)/2. Or use Area = ½ × a × b × sin(C).