Triangles have a special rule called the Triangle Inequality Theorem that connects their angles to their sides.

This rule says that in any triangle, if you pick any two sides and add their lengths together, that total must be bigger than the length of the third side.

Example:

1. Let’s look at a triangle with sides that are 3, 4, and 5 units long.
   • Let’s check:
     • $3 + 4 > 5$ (True)
     • $3 + 5 > 4$ (True)
     • $4 + 5 > 3$ (True)
   • So, these sides can definitely make a triangle!

Angle Relationships:

• In a triangle, bigger angles are always across from the longer sides.
• For example, in a right triangle (one angle is $90^\circ$), the longest side is called the hypotenuse, and it sits across from the right angle.

This rule is also important for naming triangles. There are three main types:

• Acute triangles: all angles are less than $90^\circ$.
• Obtuse triangles: one angle is more than $90^\circ$.
• Right triangles: one angle is exactly $90^\circ$.

Knowing these ideas is really important in geometry!