Hey there!
This answer is true.
It all started with, like everything else did and was governed by, religion. Remember that society was founded by religion- it controlled every aspect of daily life. For example, raining was Zeus, love was Aphrodite, and so on.
Thus, it's no surprise that acting all of this out as a means of entertainment arose. People would dance and sing on stage, and the first plays were all religious having to do with Gods and ancient Heroes. However, women were not allowed to take part in plays. Like many other parts of life in Greece, women could attend, but not take part in. The parts that required women were played by men with masks. That's perhaps where the iconic image of the masks for Broadway originated. Eventually, everything expanded. People wanted to hear more, and dramas, comedies, and tragedies came to be. They were stories of incredible heroes, horribly mishaps, and comical characters. Over time, Greeks came to adore the theatre and even pioneered a method of creating a venue displayed in the Theatre of Dionysus (the god of wine, and wine was a very prominent beverage in these times). You've probably seen it- it was curved-- so everybody could see and hear.
Greek playwrights eventually inspired other civilizations like the Romans- who had more violent methods of entertainment, and eventually William Shakespeare who ended up writing amazing plays such as Macbeth and Julis Caesar. It even inspires playwrights today.
Hope this helps!