Which of the following triangles cannot exist?

(a) acute isosceles triangle

(b) right isosceles triangle
(c) right obtuse triangle

(d) right scalene triangle

(e) scalene obtuse triangle
The sum of the three interior angles of a triangle is $180^{\circ}$. Therefore, if one of them measures $90^{\circ}$, the sum of the other two is $90^{\circ}$, and thus they cannot be greater than $90^{\circ}$. Therefore, there are no right-angled obtuse triangles. The following examples of side lengths show that the other cases can occur:
(a) $2,3,3 \quad$;
(b) $1,1, \sqrt{2}$;
(d) $3,4,5, \quad$;
(e) $3,4,6$.