a) A triangle with two angles 40 degree that surrounds a 5 inch side.
Note that there can be multiple triangles larger than that shown above.
So you should mark the thirf column here.
b) A triangle with sides 6m, 8m, and 9m.
Since the addition of two is always greater than the third side, the triangle is possible.
Then according to Pythagorean Theorem, it will be an accute triangle. Since the length of sides are fixed, there will only be a single i.e unique triangle.
So the second column should be marked here.
c) Triangle with angle measurements 63, 44, and 83 degree.
Note that the angle sum property must be satisfied, but here the sum of the angles is not equat to 180 degrees. So the triangle is not possible.
The first column should be marked here.
d) A triangle with side 6cm, 8cm, and included angle 40 degrees.
There is only one choice to obtain the triangle. So there will be a unique triangle.
So the second column should be marked here.
e) A triangle with angle measures 60, 90, and 30 degrees.
Since the sum of angles is satisfied the triangle is possible.
However, any combination of angles is never unique. It will have multiple triangle with the same measure.
So the third column should be marked.