Simplifying the Diagrams
The carbon-hydrogen part of a fat is typically drawn like this:

But this is somewhat messy. What if we just don’t draw the Hydrogen atoms, and just leave the bonds? We’d then have to remember the convention, that a – indicates a bond to an H, but it would be simpler. We get this:
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But this is a 2-dimensional representation that’s convenient to type. What if we re-draw it to represent the 3-dimensional character of the chemical bonds? We get this:
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The Carbon atoms sort of zig-zag; they are not in an absolutely straight line. We can take advantage of this, and create a simplified diagram that just shows the shape of the carbon chain, without indicating any atoms at all, like this:
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Using this simplified diagram, it becomes much easier to describe the differences between saturated and unsaturated fats. The differences are caused by the double bonds in unsaturated hydrocarbon chains, but the effects are visible in the shapes of the molecules.
saturated:
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unsaturated, cis-configuration:

The double bond puts a kink into the molecule. This has a huge effect on the shape of the molecule.
unsaturated, trans-configuration:
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As you see, there is little difference in the shape of the trans molecule, compared to the completely saturated molecule.
The shapes of the fatty acids, in particular the kinks of cis-fatty acids, account for whether a fat is a liquid or a solid at room temperature.