Question

The lengths of three line segments are 4 centimeters, 5 centimeters, and 9 centimeters. Using this information, triangles can be constructed.

Answer 1

Well, technically yes. One can, but it would be a so-called "degenerate triangle".

-- The 4-cm and 5-cm sides are just exactly long enough to connect between the ends of the 9-cm side. So they lie flat on top of it.

-- The angles at each end of the 9-cm side are both zero.

-- The angle at the vertex where the 4-cm side meets the 5-cm side is 180 degrees.

-- The sum of the angles in the triangle is 180 degrees.

-- The altitude of the triangle is zero.

-- The area of the triangle is zero.

-- When you look at the triangle, all you see is a 9-cm line segment. The 4-cm and 5-cm line segments lie on top of it, so you don't see them.

-- You would say "There's no triangle there.".

Answer 2

No triangles can be constructed

Explanation:

we know that

The Triangle Inequality Theorem, states that the sum of the lengths of any two sides of a triangle is greater than the length of the third side

so

In this problem

`4+5>9`------> is not true

therefore

No triangles can be constructed with the given side lengths