Which bonds are formed by a carbon atom with ${\mathrm{sp}}^2$ hybridization?

Two carbon atoms join together to create a sigma bond when two${\mathrm{sp}}^2$ orbitals overlap.
When the $2p-2p$orbitals overlap, the pi-bond between the carbon atoms perpendicular to the molecular plane is established, forming two covalent bonds from each carbon atom with hydrogen.