Hello, after I saw how people likes triforce on riven I decided to create a guide for those who still think that triforce is good I'll give some maths and proof that it isn't good as you think. Thats my second guide ever so sorry if there gonna be mistakes, I'll try to repair them and my english isn't main language.

I prefer using Flash/exhaust as exhaust helps when my team member is ganking or someone is trying to catch/tower dive me. Flash is always good pick as you can get out of teamfight anytime. Also teleport isn't bad pick as it would help you to secure dragons or gank other lanes.

Greater Mark of Desolation x6 because these runes is best for every AD champ
x3 because these runes lets you harass your oponent early game (can be swapped with ArPen runes for better late game)
Greater Seal of Vitality x9 I found that HP/lvl runes works best since we are going to make armor in this build, Hp/lvl works against both AP and AD, but if you 100% are sure you gonna lane against AD or feel better with armor runes, take them...
x9 Well Mr/lvl, there isn't what to say :D
x3 these runes I take for early harassment + better last hiting. Other good possibilities is flat hp or ArPen

Masteries can be changed because every player is different and likes different things, these masteries worked best for me, but I also tried 21/0/9 or 0/21/9 and both worked good.

Well lets talk about items.
First of all I want to advice to start with and because it lets to stane at lane much longer than your enemy.
Second thing is if you can last hit EVERY single creep and outfarm your enemy then and Avarice blde can be skipped, but I realy recommend to take atleast cuz it gives you not bad amount of hp and free gold. late game must be sold and changed for any other items which feel you need.
If you will feel that you are loosing lane or being harrassed too much, get before BF Sword
can be swapped with if you feel better with it.

Late game vs heavy AP team:


Late game vs heavy AD team:
or

Late game vs balanced team:

Second build is for jungle. Since Riven isn't best jungler I realy don't recommend to jungle with her. There is tleast 10 better junglers so why we should pick Riven to jungle?
But fi you decided to jungle with riven here is Stonewall008 route and runes since I'm not good at creating routes for every single champion.

Route:
http://www.youtube.com/watch?v=9WZU9E0tAV8

Ganking:
http://www.youtube.com/watch?v=CMA-DYJW8D0

Ok.

Lets do some math.

Lets take two identical Rivens. Both level 18

One riven has Triforce

The other has a BT

Lets compare their damage

They both ult to get them the maximum amount of AD

Tri-Riv gets about 26 bonus AD from her ult, for a total of roughly 156 AD

BT-Riv gets 40 bonus AD from her ult, for a total of roughly 240 AD

Tri-riven's damage output is

143 from each use of Q

Autos are 156 + 43 from passive + 150 from Triforce proc for a total of 349

266 from each use of W

580 Max damage from wind slash

BT Riven's damage output is

256 from each use of Q

Autos are 240 + 85 from passive for a total of 325

350 from each use of W

732 max dmg from wind slash

So, Tri-Riven's
Q>Auto>Q>Auto>Q>Auto>W>Auto>E>Auto>R
would be
3020 damage


Meanwhile, BT-Riven's
Q>Auto>Q>Auto>Q>Auto>W>Auto>E>Auto>R
would be
3475 damage

Some other points i'd like to stress
BT Riven is spending 1000 less gold for 400 more damage
BT Riven has more survivability due to shield being AMAZING
BT Riven better utilizes the AOE increases of her ult to deal out even more damage
BT Riven is actually able to complete her combo faster because Tri-force has a 2 second CD between procs, Riven's passive does not.
BT Riven has LIFESTEAL WHICH BENEFITS FROM HER PASSIVE

STOP BUILDING TRIFORCE OR WORRYING ABOUT SHEEN. A BFS WILL BENEFIT YOU FAR MORE THAN SHEEN


CAN YOU STOP BUILDING IT NOW!?