有没有办法在此代码中阻止Path Traversal？

Question

I'm trying to prevent people to use path traversal on some code. I need to do this for an assigment I've been stuck on for too long. After testing the redirect I also have to check if the page "welkom'' has stayed the same.

$pagedir = "pages";

if (!isset($_GET['page'])) {
    header("Location: ?page=welkom");
    exit;
}

$page = $_GET['page'];

if (file_exists("$pagedir/$page")) {
    print file_get_contents("$pagedir/$page");
}