A triangle has three sides, three angles, and three vertices. The angles sum to 180 degrees in Euclidean geometry. Triangles are classified by sides (equilateral, isosceles, scalene) and by angles (acute, right, obtuse).

The area is ½ × base × height. The Pythagorean theorem applies to right triangles. The law of sines and law of cosines relate sides and angles in any triangle. The triangle is the simplest polygon and the most studied.

Triangles are rigid: their shape cannot change without changing side lengths. That makes them essential in construction, from bridges to bicycle frames. They appear in art, design, and navigation. The triangle is a fundamental building block of geometry.

• Three sides, three angles, three vertices
• Angles sum to 180 degrees
• Classified by sides and angles
• Rigid shape used in construction