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How can we Proof by case to prove triangle inequality? - Answers

To prove the triangle inequality using proof by cases, we analyze the possible relationships between the sides of the triangle. For two sides (a) and (b), we consider three cases: when both (a) and (b) are positive, when one is zero, and when one or both are negative. In each case, we show that the sum of the lengths of any two sides is always greater than or equal to the length of the remaining side, thereby satisfying the triangle inequality: (a + b \geq c), (a + c \geq b), and (b + c \geq a). This structured approach confirms the validity of the inequality under all possible scenarios.



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How can we Proof by case to prove triangle inequality? - Answers

https://math.answers.com/math-and-arithmetic/How_can_we_Proof_by_case_to_prove_triangle_inequality

To prove the triangle inequality using proof by cases, we analyze the possible relationships between the sides of the triangle. For two sides (a) and (b), we consider three cases: when both (a) and (b) are positive, when one is zero, and when one or both are negative. In each case, we show that the sum of the lengths of any two sides is always greater than or equal to the length of the remaining side, thereby satisfying the triangle inequality: (a + b \geq c), (a + c \geq b), and (b + c \geq a). This structured approach confirms the validity of the inequality under all possible scenarios.



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https://math.answers.com/math-and-arithmetic/How_can_we_Proof_by_case_to_prove_triangle_inequality

How can we Proof by case to prove triangle inequality? - Answers

To prove the triangle inequality using proof by cases, we analyze the possible relationships between the sides of the triangle. For two sides (a) and (b), we consider three cases: when both (a) and (b) are positive, when one is zero, and when one or both are negative. In each case, we show that the sum of the lengths of any two sides is always greater than or equal to the length of the remaining side, thereby satisfying the triangle inequality: (a + b \geq c), (a + c \geq b), and (b + c \geq a). This structured approach confirms the validity of the inequality under all possible scenarios.

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      To prove the triangle inequality using proof by cases, we analyze the possible relationships between the sides of the triangle. For two sides (a) and (b), we consider three cases: when both (a) and (b) are positive, when one is zero, and when one or both are negative. In each case, we show that the sum of the lengths of any two sides is always greater than or equal to the length of the remaining side, thereby satisfying the triangle inequality: (a + b \geq c), (a + c \geq b), and (b + c \geq a). This structured approach confirms the validity of the inequality under all possible scenarios.
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