Asimilarity between the supreme court decisions in new jersey v. t. l. o. and vernonia v. acton is that

Both are Supreme Court decisions that are connected to the provisions of the Fourth Amendment to the US Constitution.

New Jersey v. T.L.O was a decision issued in 1985. A teenager was caught smoking in a public high school and her purse was searched, where marijuana and other drug-related objects were found. She was charged for that findings. This girl claimed that such search had violated the 4th amendment which declares illegal unreasonable search. In the end, the Supreme Court declared that the search had been reasonable.

The Vernonia v. Acton decision was issued in 1995. It dealth with the establishment of random drug tests in local public schools in Vernonia, Oregon. The Supreme Court considered such test to be reasonable, due to the interest of schools on preventing teenage drug use.

The Supreme Court has to decide in both on whether the searchs were reasonable and therefore legal according to the 4th amendment, or not.  

d: their own individual powers within the new goverment