Question 384775
We start an indirect proof by assuming the OPPOSITE of what we want is true. In this case, we would assume that the obtuse angle is NOT the vertex angle.  Then we show why that is not possible!  
It is not possible because if the triangle is isosceles, then we know the angles which are not the vertex angle (the base angles) are congruent.  Based on our assumption, both of those angles would have to be obtuse.  A triangle can't have 2 obtuse angles because then there would be more than 180 degrees in that triangle (which of course, is not possible)! (ex 91+91=182) So since what we assumed turned out to be false, then that proves that what we wanted in the first place must be true; If an isosceles triangle is obtuse then the obtuse angle must be the vertex angle.  

Hope this helps!