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Sigma bonds are formed when orbitals are end to end, and pi bonds are formed when orbitals are side by side. Hybridization explains the shape and orientation of the orbitals, which is needed to see if they overlap end to end or side by side. If one bond is formed end to end ( a sigma bond), it's impossible for the second bond between the same two atoms to have two more orbitals end to end. The second bond would have to be side by side, which would be a pi bond, making the double bond a sigma bond and pi bond.
Pi bonds are formed by leftover p orbitals, so for example if an atom of carbon was double bonded to another atom of carbon (with each carbon single-bonded to another atom), the sigma bond would be sp3 hybridized and the pi bond would be 2p hybridized.
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