Gain increasing amounts of AD or AP, Adaptive over the course of the game.
+5 AD or 9 AP
+6 Armor or 8 MR (match-up)
Conqueror's AD steroid is fantastic for Riven as she has generous ratios across all of her abilities and the extra True Damage makes you incredibly difficult to itemize against.
Triumph's extra burst healing is fantastic for teamfights where you're able to burst the backline. The health with allow you to reset and continue dealing damage.
The extra bit of Attack Speed from Alacrity for perfect for assisting your ability to weave in auto attacks quickly between [Q] casts for a fast combo.
WhyCoup De Grace
Coup De Grace's execution pattern of bonus damage synergizes incredibly well with Riven [R] and can help you snowball and 1-shot backline champions.
As a mana-less champion, Riven is highly reliant on as much CDR as she can get her hands on. The Extra CDR in the mid-game assists you in getting a quick 40% while turning into additional AD for kill pressure in late game full-build situations.
Gathering Storm on Riven makes you an absolute late game monster, able to one-shot any backline champion with the right opening.