Final answer:
The goddess of discord who shrieks beside Ares in his battle chariot is known as Eris in Greek mythology, representing strife and contributing to the events leading up to the Trojan War.
Step-by-step explanation:
The goddess of discord who accompanied Ares in his battle chariot, shrieking as she participated in the tumult of battle, is known as Eris in Greek mythology.
This deity personified the strife and discord that could erupt amidst warfare. One of Eris's most famous myths involves her contributing to the events that led up to the Trojan War by rolling the so-called 'apple of discord' amongst the goddesses, which ultimately led to the Judgment of Paris.