How am I able to watch rented movies which was Purchuse on my Mac Pro on TV ?

Movies rented on your Mac can be watched on your Apple TV via the computers app, however you must ensure that they are fully downloaded to the Mac before they will show up there.

The only way to watch a movie rented on a Mac on an Apple Tv is to use AirPlay.

Use AirPlay to display video from your Mac on an HDTV - Apple Support

Rented movies can only exist on one device at a time, and cannot be transferred to a 2nd, 3rd or 4th Gen AppleTv after rental.

For ease of use, its better if you rent the movie directly on the Apple Tv.

About renting movies from the iTunes Store - Apple Support

The only way to watch a movie rented on a Mac on an Apple Tv is to use AirPlay.

That's not correct Phil. I suggest you test this for yourself as you seem quite adamant about it. Here's one I tested earlier. (I tested because whilst I KNOW it worked with the Earlier Apple TV's, I'd not actually seen it working with the Apple TV 4).

Here it is in iTunes on my Mac.

and here it is under computers on my Apple TV 4

and on my Apple TV 3

and again on my Apple TV 2

For ease of use, its better if you rent the movie directly on the Apple Tv.

I'm also inclined to question the wisdom of that statement too, depending on circumstances.

I'd say to make sure you get the most out of a rental that you rent it on the computer, that way I can watch it in the lounge, my youngest can watch it later in his bedroom and my eldest can watch it in a room with no TV (if we had one) on his iPhone. Did I mention you can watch it on an iPhone too.

Hmm, was not aware of that. As far as the Support article goes, you could transfer the rental to a first gen Apple Tv, but not any of the others.

Looking into it a bit further, it seems the Rental sync is a recent feature of Home Sharing.

A little more on how rentals worked

http://www.macworld.com/article/1153224/itunes_movie_rentals.html

With Home Sharing, and maybe even Family sharing i assume Rentals now appear on all devices in the family sharing group.

No article that mentions this though, at least that I can find.

Personally I rent directly on Apple Tv. Much easier if that's where I'm going to watch it.

Good catch Prime Minister.

Looking into it a bit further, it seems the Rental sync is a recent feature of Home Sharing.

It's been there since the day the Apple TV 2 was launched so far as I recall.

AFAIK, this had not been an option before. No mention of it in the Rental support document I linked to at all.

Just tried it though, and you are correct. So my mistake. Never new this was a thing. Since rentals can only be on one device a time, and were only transferable to a 1st gen Apple Tv before.

From what I've gathered so far, the movie has to be fully downloaded to the computer for it to appear on the Apple Tv rental section.

You learn something new every day.

AFAIK, this had not been an option before. No mention of it in the Rental support document I linked to at all.

If you search you'll find it's been mentioned numerous times over the years.

Never new this was a thing. Since rentals can only be on one device a time, and were only transferable to a 1st gen Apple Tv before.

This is where I think you might be overthinking it, the movie isn't really on more than one device, it's being streamed not transferred.

From what I've gathered so far, the movie has to be fully downloaded to the computer for it to appear on the Apple Tv rental section.

That's correct and one of the reasons it's been discussed several times over the years, people don't see it on the their Apple TV's straight away.

I guess that could be a nuisance for some who want to watch it straight away, but on the other hand it introduces a couple of advantages that raise a couple more reasons it gets brought up here. a) it can be watched on multiple Apple TV's and b) those with a poor/slow/intermittent connection speed (especially at peak times) can download it at will and watch it later, and if they want to watch it more than once it's especially useful.