A triangle is the simplest polygon you can make. It's a flat, enclosed shape with three straight sides, three corners (called vertices), and three inside angles. Every triangle, no matter its shape or size, has a fundamental property: its three interior angles always add up to 180 degrees. This is a hard and fast rule in geometry.

One way to categorize triangles is by looking at the lengths of their sides. Are they all the same, are two the same, or are they all different? This gives us three distinct types.

Think of it as the most symmetrical type of triangle. All sides are identical, and all angles are identical too.

An easy way to remember this is that an isosceles triangle has two sides that are 'in cahoots'—they're the same length. The third side can be shorter or longer.

This is the most general type of triangle. No special treatment here; every side has its own unique length.

Another way to classify triangles is by their largest internal angle. This also gives us three categories.

These triangles have sharp, pointy corners. No single angle is very wide.

Right triangles are fundamental in trigonometry. They have a perfect square corner. The two sides that form the right angle are called legs, and the longest side, opposite the right angle, is the hypotenuse.

These triangles have one wide, open angle. Since the total degrees in a triangle is 180, it's impossible to have more than one obtuse angle.

Understanding these basic types is the first step. With these definitions in hand, you can start exploring more complex ideas in geometry.