Triangle

A triangle is a flat shape with three straight sides and three corners. Each corner is called a vertex, and each corner has an angle inside it. The triangle is one of the simplest shapes in geometry, but it is also one of the most useful. You can find triangles in bridges, roofs, bicycle frames, and even the pyramids of Egypt.

Triangles are sorted into groups based on their sides or their angles. When sorted by sides, there are three kinds. An equilateral triangle has three sides of equal length. An isosceles triangle has two equal sides. A scalene triangle has three sides that are all different lengths.

When sorted by angles, there are also three kinds. A right triangle has one square corner, called a right angle, that measures exactly 90 degrees. An acute triangle has three angles that are all smaller than 90 degrees. An obtuse triangle has one angle bigger than 90 degrees.

The three angles inside any triangle always add up to 180 degrees. This rule is true for every flat triangle in the world. If you know two of the angles, you can always figure out the third by subtracting from 180.

Triangles are special because they hold their shape. If you build a square out of sticks and push on one corner, the square bends into a slanted shape. A triangle made of sticks does not bend. The three sides lock the angles in place. This is why engineers use triangles in bridges, towers, and roof frames. The Eiffel Tower in Paris is built almost entirely from thousands of metal triangles.

A famous rule called the Pythagorean theorem works only on right triangles. It says that if you square the lengths of the two shorter sides and add them, you get the square of the longest side. Builders use this rule to make sure corners are perfectly square.

Triangles also help us measure things we cannot reach. Surveyors use a method called triangulation to measure the height of mountains and the distance to faraway points. Astronomers use the same idea to measure the distance to nearby stars. By forming triangles between known points, they can calculate distances of trillions of miles. A shape with only three sides turns out to be one of the most powerful tools in math.