Select the correct answer from the drop-down menu.
The lengths of three line segments are 4 centimeters, 5 centimeters, and 9 centimeters.
Using this information,
triangles can be constructed.

  0 or 1

Step-by-step explanation:

The answer to this depends on the version of the triangle inequality your author uses.

If you require ...

  4 + 5 > 9 . . . . .  false; NO TRIANGLES can be constructed

On the other hand, if you allow ...

  4 + 5 ≥ 9 . . . . . true; ONE TRIANGLE can be constructed

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Please consult your lesson materials to see which answer is expected.

Comment on a 4, 5, 9 triangle

A "triangle" with sides of lengths 4, 5, and 9 will look like a line segment. It will have zero height, hence zero area. Some authors don't consider such a figure to be a triangle.