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I know this could be solved using delta-to-y transformation, but I want to solve this using symmetry.

Considering the middle line the symmetry axis this becomes:

schematic

simulate this circuit – Schematic created using CircuitLab

Then, you see the we have the equivalent resistance: (1 + 0.5 + 0.5) + (0.5) = 2.5 ohms.

What's the problem?

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If you draw it a bit different, it's easy to see that there is no current flowing through the middle resistor. (It's a bridge with equal R's in all the arms.) So you can remove the central R from the circuit. From there it's easy.

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First add the 1 ohm resistances which are in direct link with arms a,b. That gives 2 ohm . Now for the rest of the circuit , its a wheatstone bridge with an equivalent resistance of R = 2*2/(2+2)=1 ohm. Adding all three we get Req=1+1+1=3 ohm.

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