Tell wether it is possible for the sides of a triangle to be.

To determine if a set of three sides can form a triangle, we use the **Triangle Inequality Theorem**. This theorem states that for any triangle, the sum of the lengths of any two sides must be greater than the length of the third side. In other words, for three sides \(a\), \(b\), and \(c\) (where \(c\) is the largest side):

\[
a + b > c
\]
\[
a + c > b
\]
\[
b + c > a
\]

If all three of these conditions are satisfied, then the sides can form a triangle. If any one of these conditions fails, the sides cannot form a triangle.

If you have a specific set of side lengths in mind, I can help you apply this theorem to check whether a triangle is possible with those sides.

Do you have any particular side lengths you'd like to check?

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Here are 5 related questions to expand on this topic:
1. What happens if the sum of two sides equals the third side?
2. Can the sides of a triangle have negative lengths?
3. How does the Triangle Inequality Theorem apply to right triangles?
4. What are the types of triangles based on their side lengths?
5. How can you determine if a triangle is isosceles using side lengths?

**Tip:** Always remember that the longest side in a triangle must be shorter than the sum of the other two sides!

Explore how to determine if a set of three sides can form a triangle using the Triangle Inequality Theorem. Learn about the conditions where triangle formation is possible and the significance of the theorem in geometry.

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