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Fury Of The Dragonborn
All auto attacks enhance Shyvana's abilities in some way.
Shyvana has a very special passive. It's effectiveness varies greatly depending on how you play and use her abilities. Due to the vast information however, the benefits of  Shyvana's passive will be explained under her abilities.

• Investing in attack speed items, runes, and masteries is a great way to increase the effectiveness of her passive.
• Attack damage, though not directly effecting her passive, is beneficial for Shyvana and her passive which relies on her basic attacks.
• Movement speed can be effective for getting in close enough to attack enemies with basic attacks for the enhanced benefits.

Twin Bite
Shyvana's next auto attack will hit twice in quick secession.
Twin Bite is Shyvana's "Q" ability, and is a great ability to enhance her damage output. When activated, Twin Bite causes Shyvana's next auto attack to quickly hit twice. The second attack will deal a percentage of her damage. Both attacks can and will deal on hit effects, like stacks from Black Cleaver or Guinsoo's Rageblade, or bonus damage like from Malady or Wit's End. 

Cooldown: 10/9/8/7/6 seconds

Second Hit Damage: 80%/85%/90%/95%/100% of Total Attack Damage
Auto attacks cause Twin Bite's cooldown to be reduced by 0.5 seconds. This effect does not occur when attacking structures.

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Burnout
Fire swirls around Shyvana deals magic damage to all nearby enemies.
// followed by a more in-depth explanation of the ability

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Flame Breath
Straight fire skillshot that does magic damage to the first enemy hit.
// followed by a more in-depth explanation of the ability

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Dragon's Descent
Shyvana transforms into a dragon and gains an additional effect on her other abilities.
// followed by a more in-depth explanation of the ability

• // state a tip/trick of the ability here
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ATLERNATIVE:

CORE:

• Trinity Force is an incredibly valuable item, despite also granting mana, which is useless on Shyvana. The attack damage, health, slow, AP, 150% bonus damage, attack and movement speed from Phage, Sheen, and Zeal respectively, more the makes up for the small mana you gain.
  
• On Shyvana attack speed is pretty much cooldown reduction for Twin Bite and Dragon's Descent. Wit's End grants a decent attack speed, some magic resistance, and two on hit effects. The first effect being bonus magic damage each hit, and the second being a short boost to the base magic resistance. With these benefits, all at a cheap gold price,  Wit's End is an excellent item for Shyvana.
  
• Granting Shyvana life steal and spell vamp, the Hextech Gunblade is a must have. Life steal from Twin Bite, and spell vamp from Burnout, Flame Breath, and auto attacks against targets debuffed by Flame Breath, the Hextech Gunblade will grant health to Shyvana from all forms of damage she can dish out.

SITUATIONAL:

• In my opinion, Berserker's Greaves are the most useful boots for Shyvana. Granting her attack speed, and thus faster way to proc her passive on her given abilities.
• Instead of Berserker's Greaves, Ninja Tabi are also a good choice. Only if most of the enemy team consists of AD champions would I build this over Berserker's Greaves.
• Like Ninja Tabi but for enemies that deal magic damage. However, with an added 35 Tenacity, Mercury's Treads are great for enemies with a large amount of good CC moves (like stuns, snares, slows, etc.) [note: Tenacity does NOT work on suppressions like: Impale, or Infinite Duress)

AD:
or or 

• The Infinity Edge grants a great 80 attack damage, critical strike chance, and increases the amount of damage the critical strikes can deal. On Shyvana this is a fantastic item, and can crit twice with Twin Bite if your lucky enough, definitely a must buy for Shyvana.
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AP:
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DEFENSIVE:
or or or

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HYBRID:
 or

• Guinsoo's Rageblade provides both AD and AP which is perfect for a Hybrid Shyvana. On top of that each time you use an ability or hit an enemy target you generate a stack, and each stack increases your AP and attack speed.
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