How is Romeo a tragic hero?

The term "tragic hero" was original defined in Aristotle's Poetics on the basis of the nature of the protagonists of Greek tragedy. For Aristotle, a tragic hero was a noble individual, greater than ordinary people, who possessed a character flaw and suffered a reversal of fortune. Although the tragic hero was flawed, he still needed to be sufficiently admirable and sympathetic that his downfall would evoke fear and pity in the audience.
Romeo fits this definition because he is a member of the nobility and a protagonist of the drama. He is loyal to his friends and capable of deep passion, but he is a flawed character in being somewhat impetuous and emotionally volatile. He suffers a reversal of fortune in the play, and most members of the audience pity the star-crossed lovers and are saddened at their deaths.