Edit: house was finished in 1984
Judging by the pictures and age of the home I would conclude that you do have asbestos.
A reference site appears to have the same tile you've provided (http://www.greatenvironmental.com/accoustic.html)
If you are doing any renovations STOP everything, get a qualified professional to come visit the site to do a visual inspection OR place a tile in a garbage bag and bring it to them.
A building inspector or qualified contractor can easily confirm this without the need to do lab testing.
If they confirm you have asbestos, you will need to have them remove it by following your local codes and protocols to deal with this.