I wrote "my father convinces." if משכנע is an adjective, then I'm wrong. I'm guessing it's a verb because it's in the verb section. If so, "is convincing" is a half a sentence, it needs an object. Anyone care to enlighten me?
It's both an adjective and a verb. The distinction between adjectives, verbs, nouns and adverbs is much less fixed in Hebrew than in English.
This brings up a few issues. First, if it is meant to be only an adjective, it should be struck from this section that is only about verbs. Otherwise, there should be advice in the tips & notes section on this construction.
Second, the example you give uses the present progressive tense which is written exactly the same as in the adjectival form given in the answer. Therefore, it is possible for the learner to assume that it still acting as a present tense verb in this question.
Third, I disagree that "convincing" is strictly a transitive verb, although I agree it is most commonly used that way in English.
Fourth, there are so many awkward sentences on Duolingo, that I find that taking a hardline on this answer is the exception rather than the rule. For example, in many different languages, there is a question that translates to "they are giving apples", which without an indirect object, sounds very peculiar to my ears.
We actually do use it without an object like this sometimes... "He's pretty convincing." "She can be convincing when she wants to be."