The Triangle Inequality Theorem tells us some important rules about triangles.

For any triangle with sides of lengths ( a ), ( b ), and ( c ), these three things must be true:

1. ( a + b > c )
2. ( a + c > b )
3. ( b + c > a )

Why It's Important in Geometry:

• Making Triangles: This theorem helps us know if three lengths can actually make a triangle.

• Use in Real Life: It is very important in areas like engineering, building design, and even computer graphics.

• Trustworthiness in Shapes: Almost all triangles we see in geometry fit these rules, which shows we can rely on them.

Knowing the Triangle Inequality Theorem is really important for solving problems about triangles and understanding their properties.