Discussion
In a ΔABC, if \(AB \lt BC \lt CA\), then which of the following is true?
Answer: A
The true statement is \(AB + BC \gt CA\).
By the triangle inequality, the sum of any two sides of a triangle is greater than the third side. That applies in particular to the two shorter sides compared with the longest, CA.
If AB + BC were less than or equal to CA, the three points could not form a triangle. The Pythagorean relation in option D holds only for a right angle at B, which the given information does not establish.
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