Question

if three segments can form a triangle, then the length of the largest segment is greater than the sum of the lengths of the two smaller segments. answer if the length of the largest of three segments isnt greater than the sum of the lengths of the two smaller segments, then the segments cant form a triangle. if three segments cant form a triangle, then the length of the largest segment isnt greater than the sum of the lengths of the two smaller segments. if three segments can form a triangle, then the length of the largest segment isnt greater than the sum of the lengths of the two smaller segments. if the length of the largest of three segments is greater than the sum of the lengths of the two smaller segments, then the segments can form a triangle.

Explanation:

The triangle - inequality theorem states that for three segments to form a triangle, the length of the largest segment must be less than the sum of the lengths of the two smaller segments. The contra - positive of a statement "If A, then B" is "If not B, then not A". The correct contra - positive of the false statement "If three segments can form a triangle, then the length of the largest segment is greater than the sum of the lengths of the two smaller segments" is "If the length of the largest of three segments isn't greater than the sum of the lengths of the two smaller segments, then the segments can't form a triangle".

Answer:

If the length of the largest of three segments isn't greater than the sum of the lengths of the two smaller segments, then the segments can't form a triangle.