The Triangle Inequality Theorem is really helpful in solving problems in everyday life. It’s especially useful in areas like building, engineering, and navigation.

So, what does this theorem say?

For any triangle with sides that are different lengths, let’s call them $a$, $b$, and $c$, the following rules must be true:

1. $a + b > c$
2. $a + c > b$
3. $b + c > a$

These rules can help you check if the lengths of materials can actually make a triangle when building something.

For example, if you want to create a triangle-shaped support structure, knowing that the side lengths follow these rules will help keep it steady and safe.

Now, let’s look at a real-life example. Say you have three pieces of wood that are 4 feet, 3 feet, and 2 feet long. You want to see if you can connect them to make a triangular frame.

You can check it easily:

• $4 + 3 > 2$ ✔️ (7 is greater than 2)
• $4 + 2 > 3$ ✔️ (6 is greater than 3)
• $3 + 2 > 4$ ❌ (5 is not greater than 4)

Since the last check doesn’t work, these pieces of wood can’t form a triangle. This tells you that you need to change something before starting your project.

So, the Triangle Inequality Theorem is very important. It helps make sure that different designs and building plans will actually work!