Not sure exactly what you mean. The word 下がる appears in each example sentence.
EDIT: unless you just mean the conjugations for tense and politeness. The dictionary form of the word is always 下がる. 下 would be a different word with a different reading.
Are you talking about the context sentences? The word 下がる is in the dictonary form. In two of the sentences it has been inflected, because verbs do that, sometimes. I have bolded inflected verbs.
せかいじゅうのかぶかが下がった。
Stock prices all over the world fell.
ねつが三十七どに下がりました。
My temperature dropped to 37℃.
ズボンが下がるようにベルトをゆるめなさい。
Unfasten your belt so that your pants will hang down.
In some cases it is. In other cases it just converts for a different sound in the R column.
Some of the example sentences are written to not show any kanji you haven’t learned yet. You can write any word in kanji (if it has kanji) or kana, as you see fit, whether it’s for style, or to make it easier for non-natives and children to read.