A triangle is a polygon with three sides, three angles, and three vertices. The sum of interior angles in any triangle is always 180°. Triangles are classified by sides (scalene, isosceles, equilateral) or by angles (acute, right, obtuse).
The Pythagorean theorem states that in a right triangle, a² + b² = c², where c is the hypotenuse (the side opposite the right angle). This theorem is fundamental for finding distances and is used extensively in construction, navigation, and physics.
The area of a triangle is A = ½ × base × height. Heron's formula can find the area when all three sides are known: A = √(s(s-a)(s-b)(s-c)), where s is the semi-perimeter.
Triangle congruence criteria (SSS, SAS, ASA, AAS, HL) determine when two triangles are identical in shape and size. Similar triangles have proportional sides and equal angles, which is useful for indirect measurement.