Yeah! Out of the blue!

You can use both. "He wears underwear."

かれはパンツをはきます

かれがパンツをはきます

There's a formal way to talk about a person's underwear. Ha

Can you explain the impolite form? What about this sentence makes it that? To me it just looks like they replaced the kana with the proper kanji, but the meanings are exactly the same. It's not like using です vs だ?

It seems you might be confused. The polite form is derived from the casual/dictionary form, not the other way around.

There are three types of verbs: いちだん verbs, ごだん verbs and irregular verbs like する and くる.

いちだん verbs end in る, e.g. たべる, and are simple to conjugate. To go from casual to polite form, simply drop the る to get the ます stem, then add ます. For example, casual たべる becomes the stem たべ and then polite たべます.

ごだん verbs end with an u kana (e.g. う, く, す, etc.), e.g. はく. Note that some end in る, similar to いちだん verbs, but they are few; consult a dictionary to check which is which. To go from casual to polite form, replace the final u kana with an i kana (e.g. うto い, く to き, etc.) to get the ます stem, and add ます. For example, casual はく becomes the stem はき and then polite はきます.

Irregular verbs are irregular, so you just need to memorise their conjugations. する becomes します, and くる becomes きます.

Haku is the so called "dictionary form" and is used in casual speech with friends whereas Hakimasu is some present/future tense conjugation that is used in formal situations such as in the workplace or when meeting someone for the first time. I guess Duo focuses on the polite form first because that's the one you're most likely to use if you ever address a Japanese person as a beginner/tourist. However, because they often speak casually, it's good that Duo introduces casual forms as we strengthen our basics along the course. I hope there will be more!

All verbs end with a "u" sound in their basic form. Replacing the "u" with "imasu" (with other changes if the syllable that would created doesn't exist in modern Japanese) makes verbs like this, that don't end in "eru" or "iru", polite. As for why the plain form was used here, it was probably just to give practice with it.

Kare was this lesson, かれ = 彼

I wouldn't call it a tense (relating to time), but rather the polite 〜ます form of the verb. A little note: 履く applies to pieces of clothing below the waist, e.g. pants, shoes, and obviously underwear.

yeah, instead there's kanji for the plain form of the verb, 履く (haku/はく), which is being used in place of はきます. Even though the "official answer" above uses はきます, it's not the answer Duolingo is expecting. At least they show the new terms on hover.

I'd report this, but they don't seem to offer a way to report it.