The Pythagorean Theorem is an important rule in math, especially in geometry. It helps us understand right triangles. A right triangle is a triangle that has one angle that is exactly $90^\circ$.

Parts of a Right Triangle

1. Legs:

   • The two sides that meet to form the right angle are called the legs.
   • We often label these legs as $a$ and $b$.
   • The lengths of the legs are the straight distances between each leg, meeting at the right angle.

2. Hypotenuse:

   • The side that is opposite the right angle is called the hypotenuse.
   • This is the longest side of the triangle, and we label it as $c$.

What the Theorem Says

The Pythagorean Theorem tells us that in a right triangle:

$$a^2 + b^2 = c^2$$

• What this means:
  • $a^2$ is about the area related to the first leg's length.
  • $b^2$ is about the area for the second leg.
  • $c^2$ is about the square of the hypotenuse's length.

This theorem shows how the lengths of the legs ($a$ and $b$) connect to the length of the hypotenuse ($c$). If you want to find the length of one side, you need to know the lengths of the other two sides.

Using It in Real Life

• In real-life situations, the legs of a triangle can represent things like how tall a ladder is and how far it is from the wall.
• According to studies, about $85\%$ of 9th-grade students are able to use this theorem to solve problems.

Knowing how to find and use the legs and hypotenuse in a right triangle is very important. It helps you understand the Pythagorean Theorem better, which is a key part of geometry and trigonometry.