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Leaves grow on alternate or opposite sides of a twig. Most species have alternate arrangement. If the leaves are growing on opposite sides of a twig, there is a very good chance that the tree is a maple, ash, dogwood, Caprifoliaceae (a family), or horsechestnut (AKA buckeye). Students remember this with the acronym "MAD Cap Horse".
Alternate leaves of serviceberry.
Opposite leaves of blackhaw.
Buds usually grow where the leaf meets the twig, so they will be on alternate or opposite sides of the twig too. As these vegetative buds grow out, we start to see alternate or opposite branching patterns.
Alternate buds of white poplar.
Opposite buds of black ash.