Triangle Inequality Theorem

Definition: The sum of the lengths of any two sides of a triangle is always greater than the length of the third side.

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Example: State whether the side lengths can form a triangle- 6 inches, 9 inches, 14 inches

Solution: 

We can use the Triangle Inequality Theorem to decide if the given side lengths can form a triangle.

Step 1: Check the given side lengths to see if the sum of the lengths of any two sides is always greater than the length of the third side.

6 + 9 > 14 (true)
6 + 14 > 9 (true)
14 + 9 > 6 (true)

Step 2: All three inequalities above are true, so we know the sum of the lengths of any two sides is greater than the length of the third side.
According to the Triangle Inequality Theorem, these side lengths can form triangle.

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