The segments shown below could form a triangle 1 8 8

Yes. 

To form a triangle every side must be smaller in length than the sum of the two other sides. 

For example: sides denoted by a,b,c
for a triangle to form
a<b+c
b<a+c
c<a+b
Thus in the case of the Isosceles triangle with side lengths 1,8,8 the rules aforementioned are fulfilled. This means that a triangle with said side lengths can exist.