Final answer:
The inverse of the conditional statement is option D: If two angles are not congruent, then they do not have the same measure, as it negates both the antecedent and consequent of the original statement.
Step-by-step explanation:
The conditional statement provided is: If two angles are congruent, then they have the same measure. The inverse of a conditional statement is found by negating both the antecedent and the consequent. In this case, the inverse would state: If two angles are not congruent, then they do not have the same measure. Thus, the correct answer is option D: If two angles are not congruent, then they do not have the same measure.
Conditional statements are logical statements with two parts: an antecedent (if-part) and a consequent (then-part). The inverse of a conditional swaps and negates both parts. In the context of geometry, the concept of congruent angles necessarily involves them having the same measure, making this conditional and its inverse a reflection of an essential property of angles.