Triangle Inequality Theorem

The Triangle Inequality Theorem states that any side of a triangle is always shorter than the sum of the other two sides. This makes sense when you think about it - you can't reach from one corner to another by a path longer than going directly between them!

To check if three lengths can form a triangle, we need to verify three inequalities:

• Side 1 + Side 2 > Side 3
• Side 1 + Side 3 > Side 2
• Side 2 + Side 3 > Side 1

Let's see how this works with examples. For lengths 3ft, 7ft, and 8ft, we check:

• 3 + 7 > 8 ✓
• 8 + 7 > 3 ✓
• 3 + 8 > 7 ✓ Since all inequalities are true, these lengths can form a triangle!

Try This! If you're given sides 3cm, 6cm, and 10cm, try checking if they form a triangle. You'll find that 3 + 6 is not greater than 10, so these lengths cannot make a triangle.

For finding the possible length of a third side when you know two sides (like 12ft and 8ft), the third side must be:

• Greater than the difference of the two sides: 12 - 8 = 4
• Less than the sum of the two sides: 12 + 8 = 20

So the third side could be any length between 4 and 20 (not including exactly 4 or 20).