Q: Why does triple clicking not work anymore in yosemite

Purpose of triple clicking?  Can you still double click?

As for selecting a line of text, did you select a highlight color in System Preferences>General?

(10.10)

Update to 10.10.1, repair permissions and restart your computer.

Only designating what triple clicking does in some system preference that I cannot find any longer.

Mouse preferences only has double clicking.  Never seen triple clicking in System Preferences>Mouse.   I could be wrong.  Some other user will need to confirm who is more  knowledgeable.

Are you using one of Apple's mice or a 3rd party?  Mouse wired or not?   If  you are using a 3rd party mouse contact the manufacturer.

I had never used that - running 10.9.5 on the iMac with a third party USB simple one-button mouse (quite old), I triple clicked somewhere in the middle of your answer and the entire paragraph was automatically highlighted:

Triple clicking on one sentence in the OP's post highlighted that sentence.

having this problem too since Sierra update — do we need to make the speed slower or faster?

Slower.

Unfortunately, the solution mentioned above doesn't do the trick for me. I am working with a mouse, trackpad and Wacom tablet. All of them still won't support triple clicking to select an entire sentence. Can anyone help me out?

If all of those are third party (Wacom), I'd suggest you check with their support.