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She is the perfect candidate for sheen -> triforce
When u consider her dmg u forget about her amazing passive that grants her dmg that is 0.5 of your bonus damage after every ability used + her amazing ultimate that gives her 20% dmg for 15 secs. So after u use every ability u proc sheen and your passive so your damage is well over any average melee ad (and if ur ultimate is active... qqq).
Her passive means that every ad item she takes will actually grant +50% more dmg to her every attack (if u use combo as u should).
I tried her out with classic melee glass build just to check her possible dmg with triforce (triforce, boots, yomumu, IE, phantom dancer, bloodthirster) and with her ult active she has around 420 dmg this way (without passive proc that is around 130-140 at the time totaling around 550 dmg per attack) so get your math straight. Add a sheen proc and a crit to this and oh my god!
Her base damage is kinda like lee sin, and i think that trinity is kinda must buy on him, but thats just my point of view. Like every off tank / tanky dps char, trinity force is a great item with a good mix of attributes, sustainability and it has a nice sheen proc to boost your damage for some amount every attack without having to invest in any pure dmg what would limit your survivability power.
Now i dont normally play her this way but rather go warmong + atma + trinity + bloodthirster tanky dps build. and even then i get over 300 dmg with my ult active and some badass hits with sheen procs.
If u add some flat dmg runes into the mix u will have around 90-100 dmg at lvl 1 after using a skill (passive proc counted in). Rushing sheen is then not a bad idea at all but i like to pick up a B.F. sword before it.
Like Bandicoot said before me, Blackcleaver does a better job, specially if you take movement quints.
Does riven have any ap skills ? If she has this build is awesome..
no she does not but think about how it says when ever you use an ability not only when u spend mana on one sheen increases basic attack damage so i think that this works well with the whole hit with an attack then basic attack and the same is said for trinity force