"I close the window."
閉める (しめる), to close. You are the one closing the window.
-masu formしめます -te formしめて
閉まる (しまる), to be closed. The window is the thing being closed by you.
-masu form しまります -te form しまって
閉じる (とじる) I think works both as transitive and intransitive.
TIP: most of the time "a" sounds (shimaru, agaru, sagaru) are intransitives while "e" sounds (shimeru, ageru, sageru) are transitives. Intransitives are the things having something done to them, transitives are you doing something to the things. NOT A RULE THOUGH like 分かる (understand) and 分ける (separate).
Duo won't accept kanji for this one, but will for others... It gets really confusing.