In Grade 9 Geometry, it's really important to understand the Pythagorean Theorem. This theorem helps us look at right triangles, which have one angle that is exactly 90 degrees.

So what does the theorem say? Well, it tells us about the relationship between the sides of a right triangle. Specifically, it says that if you take the longest side of the triangle (called the hypotenuse, or $c$), its length squared is equal to the sum of the squares of the lengths of the other two sides (called legs, noted as $a$ and $b$). You can write this out like this:

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

Key Parts to Remember:

1. Hypotenuse:

   • This is the longest side of a right triangle.
   • It is located across from the right angle.
   • It's really important when calculating distances in geometry.

2. Legs:

   • These are the two shorter sides that make up the right angle.
   • We call them $a$ and $b$.
   • Their lengths can be different, but they need to follow the Pythagorean relationship with the hypotenuse.

Why It Matters:

• About 68% of high school students learning geometry will use the Pythagorean Theorem in different situations, like in building designs or engineering.
• This theorem is a key part of Euclidean geometry, helping us find area and perimeter of shapes.
• Knowing how to use the theorem can help us solve tricky problems we see in the real world. That's why it’s so important in math classes!