Question 1026243

Hello, could someone please clarify the Triangle Inequality Theorem?  I am trying to determine if it is possible to construct a triangle with sides 4, 5, and 9.  If I take the long side, 9 and then add 4+5, it is not more than 9....therefore, not possible to make a triangle with these sides.  But, if I take 5+9, they do equal more than the 3rd side.  I thought the sum of the lengths of ANY two sides of a triangle is greater than the length of the 3rd side.  Am I interpreting this the wrong way??? Help, confused!  Thanks!  
<pre>The Triangle Inequality Theorem states that the 3<sup>rd</sup> side of a triangle is GREATER than the difference between the other 2 sides,
but LESS THAN their sum.
Taking the 2 sides: 4 and 5, and by letting the 3<sup>rd</sup> side = T, we get: {{{5 - 4 < T < 5 + 4}}} = {{{highlight_green(1 < T < 9)}}}. This indicates that the 3<sup>rd</sup> side, 
T (in this case, 9) MUST be > 1 but < 9. However, the 3<sup>rd</sup> side is 9, so such a triangle is IMPOSSIBLE to construct