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Can these following networks be aggregated to one network? If no then why? If yes then what would be the supernet mask?
Network1: 1.2.0.5/24
Network2: 1.2.1.7/24
Network3: 1.2.2.9/24

How can

1.2.0.5/24
1.2.1.7/24
1.2.2.9/24

be in same network?

I think they are 3 different networks.

1.2.0.0/24
1.2.1.0/24
1.2.2.0/24

Their sizes are same.
So sorry bro.. I have read the question wrong you are right there are three network network of size 256 each.
edited

The number of blocks for supernetting must be power of 2 . Here we have 3 blocks which is not power of 2 so we cant aggregate them to a single supernetting network but still we can reduce no of entries in router by combining first  two or last two network and they both combinely use as superneting.

Say ,

network 1: 1.2.0.0/24

network 2:    1.2.1.0/24

network 3:    1.2.2.0/24

we can combine the first two network as 1.2.0.0/23

and last network 1.2.2.0/24

this two can be entries in the router which we minimize from 3 to 2 entries.

1.2.0.0/22 is divided into 1.2.0.0/23 and 1.2.2.0/23 And further 1.2.0.0/23 divided into 1.2.0.0/24 and 1.2.1.0/24,

And 1.2.2.0/23 is divided into 1.2.2.0/24 and 1.2.3.0/24

we get four networks by VLSM