the minimum number of test cases = 1.6 * number of inputs sounds ridiculous to me.

For any given three points (input size = 3 ? ) to test if they form a triangle or not, the following two tests are SUFFICIENT.

1. Measure distance between the points, taking two points at one time. So you will have 3 values of length, none of them should be zero.

2. All the three points should not fall on a same straight line. To test this, measure the angle subtended by two points at the third point. You will get three values of angles. None of them should be 180 degrees.

it depends on the triangle .

for any triangle : La +Lb+Lc = 180 [deg]
a<>0 ,b<>0 c<>o
a,b,c - should not be in same line

a=b=c [if equilateral triangle ] and a+b=b+c=c+a
a+b>=c [always]
[a2 +b2]=c2 [ right angle triangle