"Curriculum" gets "vitae" because vitae is the genitive (possessive) form of vita, if my high school Latin serves correctly. So "curriculum vitae" means "course of [my] life."

"The term curriculum vitae means "course of life" in Latin. While it is appropriate to write either curriculum vitae or just vita, it is incorrect to use the phrase curriculum vita, the form vitae being the genitive of vita. The plural of curriculum vitae is curricula vitae."
( Look for Résumé--the accents won't paste properly).