A triangle is a shape with three straight sides and three angles. A right-angled triangle, or just a right triangle, is a special kind that has one angle measuring exactly 90 degrees. This 90-degree angle is often called a "right angle," and it looks like the corner of a square or a book.

The sides of a right triangle have special names. The two sides that form the right angle are called the legs. The third side, which is always the longest and is opposite the right angle, has a unique name.

Besides the hypotenuse, the other two sides—the legs—can also be described based on their relationship to the other angles in the triangle. These other two angles are always smaller than 90 degrees.

Let's pick one of these smaller angles and call it our reference angle. From its perspective:

• The opposite side is the one directly across from it.
• The adjacent side is the leg right next to it that isn't the hypotenuse.

These labels are important because they change depending on which of the two smaller angles you're focusing on. The side that is opposite one angle is adjacent to the other. The hypotenuse, however, is always the hypotenuse.

A key rule for any triangle is that its three angles always add up to 180 degrees. Since a right triangle uses up 90 of those degrees for its right angle, that leaves just 90 degrees for the other two angles to share.

For example, if one of the acute angles is 40 degrees, the other must be 50 degrees, because $40 + 50 = 90$. This fixed relationship between the angles is one of the most useful properties of a right triangle.

Let's review these key terms before we move on.

Ready to check your understanding?

Now that you can identify the parts of a right triangle and understand its basic properties, you're ready to explore one of the most famous theorems in all of math.