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A sigma bond ( σ bond) is a bond formed by the overlap of orbitals in an end-to-end fashion, with the electron density concentrated between the nuclei of the bonding atoms. A pi bond ( π bond) is a bond formed by the overlap of orbitals in a side-by-side fashion with the electron density concentrated above and below the plane of the nuclei of the bonding atoms.
They relate to resonance structures because sigma bonds are typically single bonds and double bonds are typically formed from one sigma and one pi bod. Depending on which area of electron density you place the pi bond, there will be different resonance structures.
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