Triangles come in all shapes and sizes, but one special type forms the backbone of geometry and trigonometry: the right-angled triangle. Its defining feature is simple but powerful. One of its three angles is a perfect 90-degree angle, like the corner of a square or a book.

This single 90° angle dictates the entire structure of the triangle and gives its sides special names. Because all three angles in any triangle must add up to 180°, the other two angles in a right triangle must be acute, meaning they are both less than 90°.

The sides of a right triangle aren't just called sides. They have specific names based on their relationship to the right angle.

The two sides that meet to form the 90° angle are called the legs. They are perpendicular to each other.

The third side, which is always opposite the right angle, is called the hypotenuse. It is always the longest side of the triangle.

Think of the legs as forming the corner of a room, and the hypotenuse as a plank of wood leaning across that corner. No matter how long you make the legs, the hypotenuse will always be the longest of the three sides.

Being able to quickly identify the legs and the hypotenuse is a crucial first step for working with right triangles. This distinction is the key that unlocks many important relationships in geometry, including the famous Pythagorean theorem, which we will explore next.

Time to check your understanding.

Now that you can identify a right triangle and its parts, you're ready to see how they relate to each other.