At its core, a triangle is one of the simplest shapes in geometry. It's a type of polygon, which is just a fancy word for a flat, two-dimensional shape made of straight lines. Specifically, a triangle has three straight sides that connect at three points, called vertices.

Every triangle has three sides and three interior angles. We often label the vertices with capital letters (like A, B, and C) and the sides opposite them with corresponding lowercase letters (a, b, and c).

One of the most fundamental rules in geometry is that the sum of the three interior angles in any triangle is always 180 degrees. It doesn't matter if the triangle is long and skinny or wide and short. If you add up its three angles, you will always get 180°.

Imagine cutting out a paper triangle. If you tear off the three corners and line them up next to each other, they will form a perfect straight line, which is an angle of 180°.

Not just any three lines can form a triangle. For three segments to connect and create a closed shape, they must follow a specific rule known as the Triangle Inequality Theorem. The rule is simple: the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.

Think of it like this: if you have two short sticks, say 3 inches and 4 inches long, they can't connect to form a triangle if the third side is 8 inches long. They just won't reach each other. The longest they could stretch is 7 inches when laid end-to-end in a straight line.

This rule must be true for all three combinations of sides.

These basic properties are the foundation for everything else we can learn about triangles. They define what a triangle is and the fundamental rules that govern its shape and size.