Why Must Electron and Positron Have Equal Angles in Annihilation?

[amy andrews]

Hi everyone,
I'm currently studying a bit of quantum theory and I came across this paragraph: When an electron collides with a positron, it moves with an angle theta_1 with the normal. Ditto for the positron, except that it has an angle theta_2. But the two angles must be equal. Why? Conservation of momentum.
Well, that was all the explanation given, and I don't understand the reasoning behind it, so could someone explain it to me? It would be very helpful during my self-study. (See the attached diagram)

Thank you!

 

[phinds]

I can't formulate it for you mathematically, but since they have the same mass, wouldn't you EXPECT them to have the same angle?