Triangles

A triangle is a polygon having three sides and three interior angles. The interior angles of a triangle always sum to 180°.

Triangles can be classified in a few ways. One way to classify them is by the number of sides of equal length:

• An equilateral triangle has three equal sides and three equal angles
• An isosceles triangle has two equal sides and two equal angles
• A scalene triangle has all sides of different length.

Triangles can also be classified by the measurement of their largest angle:

• If the largest angle is less than 90°, the triangle is an acute triangle.
• If the largest angle is greater than 90°, the triangle is an obtuse triangle.
• If the largest angle is a right angle (90°), the triangle is a right triangle. Right triangles obey the Pythagorean theorem; if c is the length of the hypotenuse (the side opposite the right angle) and a and b are the lengths of the other two sides, then the following relationship holds: a² + b² = c².

Triangles have many important practical applications. A triangle, unlike other polygons, is rigid. You can see this for yourself if you get some straws and some large marshmallows. If you make a triangle by taking three straws and attaching them at each vertex using balls of clay or large marshmallows, you will find that the shape is rigid; you cannot deform it by pushing or pulling the sides. On the other hand, if you construct a square using four straws and four marshmallows, you can easily deform it. Because of the sturdiness of triangles, they are used frequently in construction. To take one example out of many, a truss bridge will be comprised of a large number of triangles.