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Determine if each statement is always, sometimes or never true. Explain your reasoning The sum of the two shortest sides of a triangle must be less than the longest side.
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Q. Determine if each statement is always, sometimes or never true. Explain your reasoning The sum of the two shortest sides of a triangle must be less than the longest side.
- Identify Statement: Identify the statement to analyze: The statement given is ＂The sum of the two shortest sides of a triangle must be less than the longest side.＂
- Recall Theorem: Recall the Triangle Inequality Theorem: The Triangle Inequality Theorem states that the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
- Compare to Theorem: Compare the statement to the theorem: The given statement contradicts the Triangle Inequality Theorem. According to the theorem, the sum of the two shortest sides must be greater than the longest side, not less.
- Determine Truth Value: Determine the truth value of the statement:Since the statement contradicts a fundamental theorem of geometry, it is never true.
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