A triangle is one of the simplest shapes in geometry, but it's also one of the most powerful. It's a polygon with three sides, three corners (called vertices), and three inside angles. Every complex structure, from bridges to buildings, relies on the strength and stability of triangles.

Understanding triangles starts with learning how to categorize them. We can classify triangles in two main ways: by the length of their sides and by the size of their angles.

Looking at a triangle's sides is the first way to sort them. There are three possibilities.

An interesting fact about equilateral triangles is that all their angles are equal too. The same goes for isosceles triangles: the angles opposite the equal sides are also equal.

The second way to classify triangles is by their interior angles.

A triangle can only have one right or one obtuse angle. If it had more, the sides wouldn't be able to connect to form a closed shape.

Often, a triangle gets two names, one for its sides and one for its angles. For example, you can have a right isosceles triangle, which has a 90° angle and two equal sides.

Here's one of the most important rules in all of geometry: the three interior angles in any triangle always add up to 180 degrees. This is true for every single triangle, no matter its shape or size.

This property is incredibly useful. If you know the measure of two angles in a triangle, you can always figure out the third. For example, if you have a right triangle (one angle is 90°) and another angle is 30°, the third angle must be 60°. Why? Because 90 + 30 + 60 = 180.

This simple rule is a cornerstone of geometry and trigonometry, providing a starting point for solving much more complex problems.