I am pretty new to using the RewriteRule, so I am likely missing something obvious, but I have a PHP script that takes URL variables like this:
{baseurl}prop
If you look at your rule ^properties/([0-9A-Za-z]+)/$ you see that it needs to end with a forward slash. You can either remove that or make it optional like ^properties/([0-9A-Za-z]+)/?$.
^properties/([0-9A-Za-z]+)/$
^properties/([0-9A-Za-z]+)/?$