#### Answer

$G$

#### Work Step by Step

An obtuse triangle has an obtuse angle as one of its interior angles. If the sum of all the interior angles in a triangle is $180^{\circ}$, and if one of those angles is more than $90^{\circ}$, then the other two angles must add up to less than $90^{\circ}$. With this in mind, let's take a look at the options given:
I. cannot be true because we cannot have a right angle in this triangle when one of the other angles is already greater than $90^{\circ}$.
II. is true because each of the two remaining interior angles has to be less than $90^{\circ}$, which is the definition of an acute angle.
III. is true because an obtuse triangle must have an obtuse angle in it.
IV. cannot be true because a triangle cannot have vertical angles.
Therefore, numbers II and III are true. This corresponds to option $G$.