Mr. and Mrs. Paul Lilley of Gatesville announce the engagement of their daughter, Rachel, to Travis Badgett, son of Mr. and Mrs. Jimmy Badgett of Gates.  Rachel, a graduate of NC State University, is a teacher at Providence Grove High School in Climax, NC.  Travis is also a graduate of NC State University and works with the USDA in Reidsville, NC.  An October wedding is planned.