Solving Truss Force Issue: CD & DE Equal to 0?

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In the attached problem, I don't understand why members CD and DE are equal to 0. I was under the impression that the combined vertical components of BC and CD should equal 6+downward components of BC and EF, as to counteract the force straight down, but this is not the case.

My questions:

Why are the forces in members CD and DE equal to zero?

If they are equal to 0, what stops the downward force from moving the structure?

Thank you

Note: G and Ay are 6 and 6, not 8 and 6 as shown. I used the right values for my calculations, but for some reason wrote 8 down
 

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Sorry yes - that's what I meant.
 
The answers in the back of the textbook
 
IF THE STRUCTURE AND LOADING ARE BOTH SYMMETRICAL THEN THE EQUILIBRIUM OF JOINT d REQUIRES SYMMETRY OF FORCES IN cd AND de. tHAT IS THE CLUE...