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I think the main thing you need to know/most of what we learned is that one sigma bond occurs in any type of bond, single, double, or triple. For pi bonds there will be 0 in a single bond, 1 in a double bond, and 2 in a triple bond.
I think you should know that in a single bond there is 1 sigma bond. For a double bond there is 1 sigma and 1 pi bond and in a triple bond there is 1 sigma and 2 pi bonds. Moreover, sigma bonds interact end to end whereas pi bonds overlap side by side.
I think you should also know what types of orbitals form each. For example, in ethene (C2H4), there are 4 sigma bonds between 1s and 2sp2, 1 sigma bond between 2sp2 and 2sp2, and 1 pi bond between the unhybridized p orbitals.
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